I think that a more refined version of this could find its way into a lot of Feather projects, including at least one or two of my own. See if you can hunt down some ways to neaten things up a bit (like maybe finding an actual 1XAAA battery holder, and wiring it in place).

EDIT: Also see if you can figure out a way for the user to replace the battery, if needed, without pulling the Feather system apart if something's stacked on top of this Feather.

Sure, I can do that, it would require minimal effort. However, it will never be an official Adafruit Feather if only for one reason: if they start selling LiPo batteries in AAA form factor, people will start putting them into devices in place of regular batteries, and be very sad when they release blue magic smoke.

A battery-holder Feather makes sense, but it would be more of a mechanical project than electronic, and I don't have a 3D printer. Maybe you could do it, and enter the contest with it?

I have no 3D printer either. But I do think it may still work, at least in principle, even if you don't modify the project. Adafruit does already sell a battery-holding Shield for regular-sized Arduino, and I'm actually a little surprised they don't already do this. If I don't get the top prize, this one is what I'm rooting for. Seriously.

They do have their 400mAh Lipoly batteries designed for the Feather form, though I suspect that it's a bit big for something like what you've done; but their 100mAh might be doable. There are a couple of sizes in between that might work (I'm too lazy to compare measurements at the moment), and someone else might sell something in the right general shape.

I found something interesting: https://www.digikey.com/products/en/battery-products/batteries-rechargeable-secondary/91?k=&pkeyword=&sv=0&pv32=306832&sf=0&FV=46%7C29501%2C46%7C29515%2C46%7C30762%2C46%7C31900%2C46%7C31902%2C412%7C365295%2C412%7C365310%2C412%7C365315%2C1989%7C0%2C-8%7C91

Awesome project! I’m gonna have to figure out something to make for the contest too.