I went ahead and did it anyway. I was curious, and I've actually had this problem crop up before. Assuming you can Mesh > Separate (then delete history) your model to separate all the individual pieces, and also assuming that each piece only has UV information inside one of the many UV Sets, the script below will work for…
I could probably whip up a MEL script to knock that out but I would need to know a bit more. Does each UV set refer to a unique mesh element? If you were to separate all the pieces out as their own objects, would they all only have UVs under a single UV set (all UV sets but one are empty)?
Thank you so much. I had a crazy amount of UV sets. It tiled across my monitor. For me it worked great when I combined the objects I wanted to share the same UV space. I deleted history, ran your script, and deleted history again. When I first tried it I didn't delete history before running it, I waited for about 5 minutes…