I have the same bath/shower in my '74 as your '72, it would appear, and I think that you're going to have to open up that wall some more to do any repairs.
Anyway, last winter, I missed part of the winterizing and froze the short pipe that feeds the mixed water to the flexible hose for the shower "telephone" handle. It split about 2 or 3 inches along its length, and of course, it leaked. It's only ~6" long, by the way.
You can see what it all looks like better in the photo in this post
. The white arrow indicates my repair.
It had been years since I soldered anything, and I don't think I had ever soldered copper pipe before, but for about $20 I was able to buy a little kit that gave me the soldering "tip" and shutoff, a cylinder of the gas that feed the tip, a lighter for it, some solder, a little tin of soldering paste. In other words, all the tools necessary to be able to solder copper pipe.
First thing I did was fire up the soldering unit, heat the connection that was holding the pipe in place, and pull it out with a large pair of piers. That was easy.
Then, I cut a piece of the pipe (the store sold small pieces of the right diameter as well as full 8' pipes) sanded the ends and the interior of the elbow, put solder paste on, poked it into the elbow that holds it, and held the flame on the elbow. When the solder paste began to sizzle, I held the solder directly on the top of the joint, and allowed the heat of the pipe to melt it. As it melted, it got sucked into the joint. I looked carefully around the whole joint, and it appeared that I had a good, complete one, so then I shut off the soldering unit. That wasn't as easy as the first step, but not terribly tough either.
After letting it cool a bit, I repeated the process to solder on the brass connector that would allow the shower hose to screw on.
Letting it all cool for about 20 minute, I screwed on the shower hose, and tried it. It all worked fine, no leaks!
I then carefully cleaned all the old gobs of dirty caulking off the plastic parts of the wall I had disassembled to get at the pipes, screwed it together and caulked it with GE silicone, and went out and bragged to my wife and neighbour about my job.
All this to make two points:
- It's cheaper to repair what broke with copper than to get involved with PEX, IMHO
- You too can solder. Hey, if I can ANYone can.
This is all my opinion of course, but I will repeat, if I can do that, anyone can. And probably better! LOL!
Good luck with your repair, and keep asking questions, you will get there on way or another!