Hello all from NY!

I've browsed for a few days and see a ton of knowledge here. I have a problem with my tub / shower. I have identified them as Sayco with a hot water knob, cold water knob, tub faucet and shower head. We just bought the house in April. It may have been casual dripping then but didn't notice. We noticed that we get a drip every 30 to 45 seconds or so from the tub faucet. I am not also noticing that when the shower or tub runs that it drip from behind the hot water handle.

I figured that if I take off the handles that I could replace the "guts" and life would be good. There in lies the problem... I cannot get the handles off. The are a metal handle and am sure they are "frozen" on. I've tried Lime Away to let it set but to no luck. I've tried tapping on the handle not luck. I've pulled on the handle as hard as I dare to no luck. I finally read about a handle puller on here that had a the long skinny end that goes inside the threaded area where the screw hold the handle on. I tried it on the hot water handle and it was turning hard and though that sooner or later it pop... nope. I pulled it back out and noticed that the end of the handle puller it probably just a little large for the hold it barely shined the threads so the screw still worked to hold the handle on.

At that point I quit. I can take some emery cloth and reduce the diameter of the end of the puller. Mu problem is this... I cannot get into the wall if something was to go bad. This bathroom shares the same wall the the master bath sink exactly on the other side so the plumbing is buried in the wall. It sucks. There is also no dedicated shut-off for this bathroom, it will need to be put in.

My questions are this:

What is the best way to get the handles off? If I use the handle puller, can I do any damage in the wall that would cause leaking? If the handle or stem breaks / gets damaged I can just replace those but I cannot get into wall (fiberglass surround).

I would appreciate any help that you all could provide.

Thanks for the time you all put in...