...I'm an old fart, aren't I?
Not as old as I. I still regularly use Paint Shop Pro 3.12 on the machines that I have that are running Windows XP. Considering that v3.11 introduced the ability to have more than just 8-character filenames with 3-character extensions, you know that's ancient. This is from the Windows 95 days... And unlike you, I do everything
except transparencies in Paint Shop Pro, which I run to GIMP or Photoshop for, the latter which I think I should spend more time on, because that can actually be put on a resume. I tried to use later versions of Paint Shop Pro, but they did some weird anti-aliasing crap I couldn't figure out how to disable, and when selecting areas, the "square" always seemed to be off a little bit, like it is (in my opinion) in MS Paint.
If the JPEG is saved at a high enough quality, and the image you're working on has 256 colours or less, you may be able to load a palette which would force the JPEG-compression-distorted colours back into their original ones.
If you can't do that, you could greyscale or invert the colours in the now-JPEG image and use it as a guide, and reconstruct your image directly on top of it. At the very least it should save time with placement/arrangement.