Devil's Gimp 2.6 and my 2.06 are the same thing, I just got used to phrasing it that way in BBS threads so it was obvious it is a prior version to Gimp 2.10. I'll stop doing it now as its just confusing people.
My method is to save the 24-bit bmp in PSP, open this bmp in Gimp, then "Layer/New Layer", check the "Transparency" button is selected, then hit "OK". Then with 2.6 I hit "File/Save as" (with 2.10 its changed to "Export as"), then click on the various windows' buttons that come up to save it. With 2.10 I then open this file in MS Paint and hit the save icon.
I just did a test with 2.6 and 2.10 plus Paint on both a 1024 res and 2048 res file. Having re-saved the file using Gimp I right clicked on its desktop icon and selected "Properties" in order to check the "Size" stat in bytes. These are the results:-
Gimp 2.6 32-bit 1024 res file:- 4,194,360 bytes
Gimp 2.10 32-bit 1024 res file:- 4,194,442 bytes
Gimp 2.6 32-bit 2048 res file:- 16,777,270 bytes
Gimp 2.10 32-bit 2048 res file:- 16,777,354 bytes
In both cases opening the 2.10 file in MS Paint and hitting the "Save" icon restored the size to the same as the 2.6 file. So if you want to make sure your 32-bit files are OK to submit just make sure their size matches the 2.6 results above.