This is a very fun, creative question. Given the fact that there are some highly quotable (and somewhat pithy) moments in the text of the novel, I'd suggest that we might look for quotations from The Great Gatsby itself for a title idea or two.
Here is a passage from early on in the text, pulled from the eNotes page of quotes from Gatsby:
"If personality is an unbroken series of successful gestures, then there was something gorgeous about him, some heightened sensitivity to the promises of life.… [Gatsby had] an extraordinary gift for hope, a romantic readiness such as I have never found in any other person and which it is not likely I shall ever find again."
From this extended quote, we might take the phrase "An Unbroken Series of Gestures" as a potential title for an essay on Gatsby's ill-fated quest to recapture the past. Alternatively, we could isolate the phrase "An Extraordinary Gift for Hope" as a title on the same subject.
Each of these phrases resonates with (1) the notion that Jay Gatsby is dedicated to a romantic and, arguably, highly unrealistic view of reality and (2) that Gatsby's greatest flaw was also his greatest virtue - the ability to dream.
This vision of Gatsby is repeated in several places in the novel and given a clear rendition when Nick confronts Gatsby on the subject of his quest.
“You can’t repeat the past.”
“Can’t repeat the past?” he cried incredulously. “Why of course you can!”
Using "Can't repeat the past?" as a title, your essay might start at the very beginning by using Gatsby's own words to describe his impossible aims. Gatsby is "The American Dreamer" dreaming the American dream, as is often pointed out in discussion of Fitzgerald's novel. So, using the idea of dreams and dreaming might also be a good way to go for the title of an essay on Jay Gatsby's romantic, idealistic and ill-fated quest.
Titles that state your primary thesis (in part or whole) and make a play on the title or a quote from the text are often a good bet. Here are some suggestions:
Ghostly Heart: Jay Gatsby's Impossible Dream
A Beautiful Little Fool: Gatsby and His Lost Past
A Bridge Too Great: Gatsby's Romanticized Past and Failed Present
A Matter of Infinite Hope: Jay Gatsby Dreams of the Past
Eternal Reassurance: Gatsby's Self-Possession and Failed Dreams
Within and Without: The Bright Dreams and Dark Realities in The Great Gatsby
In each example, the text before the colon references either the title or a quote from the book; the text that follows the colon states some part of your thesis or the focus of the paper.
I agree that this is a really interesting question. I also enjoy creating titles for essays on works of literature that include quotations from the works in question, or play on imagery or dialogue from the texts. Given your topic, on Gatsby's unobtainable dreams, I think it might be interesting to include discussion of Daisy Buchanan in your thesis, since she is such a big part of Gatsby's motivation. So here are some ideas captured in titles and brief descriptions of how they might work:
"I've Never Seen Such Beautiful Shirts Before": Daisy Buchanan's Lost Dreams of Romance (Daisy's moment of sadness and catharsis, when she weeps over Gatsby's many beautiful shirts, shows she regrets rejecting his proposal of marriage when he was but a poor soldier, and now realizes he gained wealth in order to make her happy.)
"Rich Girls Don't Marry Poor Boys": Daisy Buchanan's Self-Absorbed World (This idea examines Daisy's self-centered behavior and its impact on others, including her rejection of Gatsby for a richer man, her willingness to cheat on her husband with Gatsby, and her failure to take responsibility for the fatal car accident that leads to Gatsby's murder.)