Cheers! Welcome to the forums. For the resolution, the reason 1280x720 isn't supported is simply that we need 768 height of space in order to fit all the elements. The game takes up IIRC 704 pixels, and then the HUD takes up exactly 64. Anything less than 768 makes it so that you're either cropping stuff, or else we'd have to do scaling on the main game graphics and that tends to look really bad (pixel art gets really blurry in those circumstances).
Regarding the HUD, certainly on 1280x720 there would be some room on the sides for some of the elements (buttons, life, items, etc), but there wouldn't be room for the text that shows unless we put the playable area oddly off to the side or something.
Generally speaking, I think that 1440x900 is the best 16:9 resolution to use here. Either that, or even a 16:9 monitor should support 1024x768 with black bars on the side. That should solve the stretching problem, although honestly I'm not sure why 1280x768 is stretching in the first place. There is a bit of an issue with the graphics looking stretched as soon as you change screen resolutions that I need to fix this week, so it might be that you can just switch to 1280x768, close the game, reopen it, and all will be well.
Hope that helps!