So I designed my game to be similar to a black cartridge, whereas its playable on a DMG in monochrome, and on a GBC in full color.  Unfortunately, while it runs great on a GBC, the lag is horrible on the DMG.  So my plan is to release two versions of the game, one with full color (because it would be a shame to throw all that work out the window).  And another one that would be strictly 4-color, using the DMG palette specifically for the jam.  So both versions would uploaded, as both .gb and .pocket files.  I can only upload a single web version, so I figured I would do that in full color.  Would this be allowed?

no. you can upload the full color version separately if you want, but your jam submission needs to follow the rules of the jam. also you don’t need to have a game that plays on actual hardware, just a web or windows build is fine.

I really like the idea, but as the others have clarified it's best to not confuse people rating the game. Definitely upload the files once the jam is over though (or sooner, if you like, as a separate page - you should probably do this anyway so people get a suitable notification for it)