Piano Hinge
Yes, in my opinion you can use LP4-3 pop rivets for the floor pan to piano hinge attach. However, a couple of things to try with the AN470-4-4s before you give up on them:
1. Make sure the parts (floor pan and hinge in this case) are well secured before riveting. I try to clamp these sorts of assemblies to the bench, or the workmate so they don't move around when driving the rivets.
2. Try some Snap-Soc rivet set caps (try Avery). I found these really helped cushion the rivet heads and helped keep the rivet set centered.
3. Make sure the rivet gun or air regulator to the gun is set properly. Too much air pressure will make the set jump off the head. Try some test parts/rivets to get the pressure where you want it.
4. Try a tungsten bucking bar. I can't remember when I last used my cast iron bucking bars. The tungsten bar is so much denser, easier to control, and does not tend to bounce off the shop head.