That's a great-looking frame, really liking that! So, firstly why do other calipers not fit, is that not fitting onto the disc, or how the calipers fit to mount to the frame? Secondly, why doesn't the existing function? Do you just mean the pads won't squeeze down to grab the disc when you depress the brake pedal?
Firstly: There are different thicknesses of brake discs, and of the calipers to use with them. If the new calipers are too tight to fit onto the disc properly, then the disc is too thick for them...........(and it's pretty tiny, for example I'm running an 8" diameter). If it just doesn't use the same bolt holes, then you have to make new bolt holes or whatever mods necessary to mount one of the new calipers.
Secondly: Does the caliper move when the brake pedal's depressed if it's not mounted on the disc? Until there's no doubt whatsoever that every cubic nanoliter of air has been purged from the system, you can't condemn the caliper. I'll make a gentlemen's bet with you right now that air in the system is all that's wrong with those brakes. At least I hope so.