Buy a large oven cooking bag at the grocery store. Get the one for turkeys. Plenty of room to work and no lose no parts.
Once the firing pin is forward a slight tap while pulling the safety. Once it moves out a little rotate slightly and pull out. Something I have run into concerning the heavy hammer cocking. remove the insert pin and backstrap, hammer in fired position. remove spring and plunger.It sounds like you have debris in the plunger. The hammer stirrup needs to go down into the plunger without hitting bottom when assembled. This gun sounds like it was immersed at one time into who knows what. I wish you were closer, I haven't worked on one of these for quite a while.
By the way, if I do everything at once, how would I know what specifically was wrong, or maybe that isn't so important. Just do it all at once, and it should work like new.
this is the way to do the backstrap. This is my model 39 but it's the same procedure. I make it look easy, but I have done thousands of these.
YouTube
It seems like there are a number of things going on with this gun. I personally would completely disassemble, clean and reassemble, but a model 52 has a little more going on compared to a 39 when it comes to setting the trigger stops. But it can be done. I could try to do a video with my 469. I made mine a single action with the same trigger stops as a 52.