OK so I got one of the pistons out using a bicycle pump like someone had suggested. I cleaned up the calipers and now Im wondering if I have heat sheilds in place or not. There are thin metal plates seemingly permanently riveted or bolted to the piston, but their shape is a little different from the new sheilds that came with the repair kit.

It looks to me like the new ones are actually supposed to sit in the ones that are built into the piston, am I right? The ones that are there, (the backing plate?) are a little bent here and there. Ill try and reshape them.

Ill try pushing in the piston with a c-clamp and a metal plate to see if I can get it to moe. Is it better to push it in rather than try and pull it out somehow?

Update: I managed to sueez the other piston down using a vice. It fit just right into the caliper but was pretty hard to push down. Now the chore is getting it out. How to do that now. I will have to plug the other side first obviously, but I wonder if its a sign of damage that it was significantly harder to push down than the inner calliper?
Off to bed