I did find the workflow that works for me in Photoshop and it was your comment on resoution d4v1ks, but first:
Please, let's not spiral off on a tangent, and if you don't know, this is a topic that makes an argument over magic photons or Kirk-vs-Picard look like a polite disagreement, but... the concept of "DPI" in digital image is a sort of myth, and long drawn out battles have been waged over it. I'm ONLY bringing it up to illustrate what works and doesn't work FOR me and perhaps illuminate paths forward, not to spark an argument. In my own video-professional business, 72 dpi/ppi is the standard for online/video but this was just what I was taught and I only recently read about 72 becoming 96 in Windows when the IBM 8514 came out back in the day, blah blah blah. I know it gets very confusing (it is to me) and I have no intention to teach/discuss right/wrong mythology as I have no horse in this race and I just want to know what works for me, profesionally and as a hobby. So...
Seeing you comment about trying 72 suddenly clicked that there was my problem - 72 is my default document resolution and why it was coming out stretched. Switching it over to 96 made everything I make work just fine (so much for "dpi" not mattering I suppose).
To make an image in Photoshop for the sprites and replace it, as I did in both examples:
-after making my new image, (& working in 96 pixels/inch resolution), I resized it to the same horixontal-x-vertical pixels as the image I am replacing. E.g., the splash page is 800x600, the F-DDX schematic is306x175
-save as bmp. In Photoshop, when the "BMP options" pops up, use file format "Windows" and depth "16 bit". (Under "Advanced Modes," X1 R5 G5 B5 works, A1 R5 G5 B5 does not). Name it the same as the one you're replacing ("2889", "21376")
-using the wonderful Q3 Editor (currently I'm using vers. "1.4", from 12/12/15, 1618), the images slide in like butter and look fine in-game, no noticeable shifts in centering as of yet.
I've only been working on images of ships and menus so far, so maybe I'll try something smaller like a 36x30 icon, to see how it places.