Yeah, M->LTM is a no-go (LTM->M is fine, of course). The good news is there are plenty of LTM lenses out there, and prices are down from a few years ago. I used a Jupiter-8 50/2 as the standard lens on my P for quite a while, before switching over to a Canon 50/1.5. The Jupiter-12 35/2.8 will fit, but you have to watch the rear element when you first mount it (open the shutter and watch from the back) to make sure it doesn't hit the light baffles - if it does, just tweak the baffles out of the way. The Canon 50/1.8 was the standard lens on the P back when it was new and is considered excellent; the only thing to watch for is that the later (black & chrome) lenses are prone to hazing that cannot be removed - it's actually etched glass on one of the inner surfaces. The all-chrome 50/1.8 doesn't seem to suffer from this. If you want more speed, the Canon 50/1.4 is also a very highly-regarded lens.
Note that your Industar-22 may not collapse on the P. I haven't tried that combo, but most collapsible lenses will not do so properly on the later Canon bodies.