Note: I am aware the question was asked almost a year ago, but it still hasn't been answered, and I'd like to share what I found.
TL;DR There is one, and possibly more
Legends of Maui by Westervelt
The first source I checked was the one cited in the Wikipedia article you used in your answer. (I think the section on the Wikipedia page is not, in all honesty, a good summary of the myth(s).)This is also the source that DavidPostill used in their comment(s). In the four myths mentioned in the chapter (Section III, which can be found in text form here) in which Māui successfully lifts up the sky, only one mentions a motivation resembling that of feeling sorry for the humans. This myth starts on the bottom of page 36:
The Hervey island myth, as related by W. W. Gill, states that Ru, the father of Maui, came from Avaiki (Hawa-iki), the underworld or abode of the spirits of the dead. He found men crowded down by the sky, which was a mass of solid blue stone. He was very sorry when he saw the condition of the inhabitants of the earth, and planned to raise the sky a little. So he planted stakes of different kinds of trees. These were strong enough to hold the sky so far above the earth "that men could stand erect and walk about without inconvenience."
This clearly states that Ru, Māui's father, was the one feeling sorry for the humans. The interesting part comes afterwards when Māui himself enters. It is explained that Ru was "rather proud of his achievement," and was very glad for the praise he received because of it. Māui, "not represented ... as possessing a great deal of love and reverence for his relatives," enters and ridicules Ru "for thinking so much of his work."
The full quote is below.
For this helpful deed Ru received the name "The supporter of the heavens." He was rather proud of his achievement and was gratified because of the praise received. So he came sometimes and looked at the stakes and the beautiful blue sky resting on them. Maui, the son, came along and ridiculed his father for thinking so much of his work. Maui is not represented, in the legends, as possessing a great deal of love and reverence for his relatives provided his affection interfered with his mischief; so it was not at all strange that he laughed at his father.
The legend goes on to tell how Ru threatens to "throw you [Māui] out of existence," a threat Māui dares him to follow through with. When Ru tries, Māui uses his shapeshifting abilities to get the better of his father before lifting both Ru and the sky up, and hurling "them both to such a height that the sky could not come back." This entangled Ru "among the stars."
Māui was not the one who was sorry for the humans, that was Ru. While one could argue that Māui shared the sentiment, and was mad that his father only lifted the sky up so high that "men could stand erect and walk about without inconvenience," because that wasn't good enough for the humans. This may or may not be true, and it's hard to know whether or not it is, but the way the story is told here seems to me like Māui just didn't want his father to have such a big head about lifting the sky up such a small amount. This also ties into what we know about Māui, and it seems the most likely (at least in my opinion, that is).
Other Scattered Accounts
In my search for a source documenting Māui as feeling sorry for man and being motivated by this to lift up the sky, I found myself in quite the rabbit hole.
Edward W. Gifford
An ethnographer who documented many tales from the Tonga. I was pointed to his work by "Māui: Polynesian Culture Hero. Variations of Motifs in Māui Mythological Cycle in East and West Polynesia." I was only able to preview the book itself, but it retells one of Gifford's accounts, the full version of which can be found here.
It is said that the sky was low in olden days. The elder Maui (Maui Motua) was preparing his earth oven. When he used his poker it got jammed in the sky. Then he reversed his poker and pushed up the sky until it was very high.
This is quite different from other accounts, but according to Gifford very similar to that of Philippine tales. The publication was quite brief in it's covering of Māui, and more tales than the sky-raising were told, making it hard to pick out examples. There were, however, two other mentions of lifting the sky.
The first (a portion of a poem with an English translation):
Lau koe ngataanga e langi e teve, / Pea tuu a Maui o teketeke /
Aki e u kae alu e fefine faele /
Ae langi na ka tau haele
It is said that the boundary of the sky was a teve plant, / That Maui stood and pushed up the sky / With a stick for a confined woman / So that we might under the sky walk upright
In the end, it appears this one is a dead end, as the second mention is an account from Wellington Lavaka (who, try as I might, I found nothing on) from Haakio, Vavau which only corrects which Maui it was that lifted the sky (Maui Kisikisi lifted the sky, rather than Maui Atalanga). As a side-note, Tonga Māui mythology is quite interesting, and I'm glad I was able to look into this.
This one confused me because I was unable to find a good source for the account, but it was used in two places, one a little more detailed than the other. It is very possible that there is a better source for it, as one is mentioned, but it is a book I'm unable to find the text of anywhere, and don't have the time to look into buying or borrowing a copy. If you're interested, it may be an interesting thing to look into.
In the meantime, take this one with a grain of salt because this, and this were the only sources I could find for the tale:
When Maui was a young man, the sky was so low that trees often became tangled in it, all the leaves were flattened and darkness surrounded the land. Men and women often had to crawl from one place to another because the sky was not tall enough to walk upright. Determined to change this, Maui visited a kahuna, or Hawaiian priest and healer, who tattooed him with a magic symbol on his forearm. Maui also sought out an old woman and drank from her gourd, giving him the great strength he would need to lift the sky.
After a great struggle, Maui was able to push the sky beyond the mountains, lifting the edges over the wide expanse of the ocean, where it remains to this day. His effort gave room for all creatures, plants, trees and man to grow and walk tall among nature. When dark storm clouds gather around Haleakala, it is said that they are afraid to stay for long in case Maui chooses to hurl them so far that they can never return.
Some of these claims are verifiable from other sources I'd found earlier, but others were not. The book linked was Oceanic Mythology, which seems to have only been used for a description of Māui, but is worth looking into if you have the time. More importantly, however, this is another dead end.
Māui: Polynesian Culture Hero
I already brought this book up as what pointed me to Gifford, but it's worth bringing up again. The only library I can find this book at is the University of Bristol's library, but it seems as though it is definitely worth looking into. You can also find the book on a few online sites, but it's not exactly an easy book to find. If I get a chance to look into it more, I will gladly update this post, but for now this section will remain as more of a resource than anything.
This is the last relevant source I was able to find, and it's probably the best one as well (fitting that after I do all this research, the last one I find is the best and most relevant). This one has an online version that I was able to view, and you can too (you do have to sign up for an archives account, but it's free, just gets in the way a bit).
The account in this book is found in Appendix B (dedicated to Hawaiian Legends), and goes as follows:
A very long time ago, the sky almost touched the land. The trees were pressed down, so that their leaves were flat. No one could see the hills and mountains. The Sun was so close to the earth that fields were burned by its rays. People were very uncomfortable.
Maui was the son of the goddess Hina and the god Ku. He looked at the sky pressing down on the islands of Hawaii. He looked at the burned fields. He looked at the uncomfortable people. He decided to lift the sky.
The legend continues to tell how Māui did lift the sky, giving lift after lift until it rested far above the earth. If you'd like to read the full legend, you can find it on the Internet Archive.
While the validity of the legends in Appendix B could be called into question, the book itself seems well researched (taking content from reputable sources such as the Bishop Museum, and being thoroughly peer-reviewed), and the legends told here line up with the legends we know to have come out of Hawaii and all of Polynesia. Another argument could be made that the motivation of Māui to lift the sky is not clear, which is true, but it seems heavily implied that he did it to help the people who were "uncomfortable." It is up for interpretation, however, as the motivations were not made explicitly clear.
Conclusion: There is a Source (and possibly others -- or maybe not)
After spending far too long trying to find a source for this, there appears to be one. Polynesian culture, as well as many others, are hard to study because a lot of it was word-to-mouth, and much wasn't written down until much later. For all we know, many more tales were told this way, and many more still may never be learned. Out of the many sources I found, only one told the story this way (except, as mentioned in that section, it is still open to interpretation), but there are so many more sources out there, including some I didn't get to look into myself. I thoroughly enjoyed myself doing this research, and I think that these were great peoples who deserve to be known more about. I won't go on a tangent, but thank you for giving me the opportunity to study something I otherwise might not have.