Hopefully a wall directly behind this faucet wall will have an access of some sort to get at the piping. If your house is 50 yrs. old, you will probably have galvanized pipe. If the shower is on the first floor, it would probably be wise to change the piping from the cellar up to this fixture with copper because you will probably end up having to use some copper in the change over.
One of the major companies (either Delta or Moen) makes a large plate that will fit over a hole that you would have to make to change the faucet from the tub side. The company that makes the plate has a faucet that fits perfectly into this plate. The Moen plate is called a "remodeling cover plate" and the part # should be #1920. I don't have a Delta number. Even with this, you have to be careful and not make a hole any larger than the plate will cover up. If you have ceramic tile on the shower walls, then the job gets even trickier. It would probably be a whole lot easier if you could do most of the work from the backside.

If it's just the spout and handles that are bothering you, then you could try replacing just those (not the stem assemblies). Spout is fairly easy (whole thing should unscrew off). The handles and escutcheons (cover plates behind each handle) are trickier, so take them to a good plumbing supply to match them for fit.

You may have to try more than one place. Best if you can find one with a display of handles and stuff. Maybe the internet would work in this regard, too.

BTW, I realize I didn't address your question in regard to replacing with NEW stuff - sorry about that.

It's just an alternative if changing the "look" was your primary concern, and one that avoids getting into the wall.

Bumping this question up. My plumber just told me that this Moen remodeling cover plate is what he will use to replace my leaky old shower faucets (I have 3 handles) with the new single handle pressure balancing faucet.

Can I use any Moen faucet with this cover plate? He only gave me a choice of their Chateau collection which wouldn't be my top pick.

I need to replace (for the 2nd time) the hot and cold water taps and the shower diverter tap. I want to turn the left-hand handle and get hot water and the right-hand handle and get cold water. The middle tap switches the water from tub to shower. Does this type of shower set-up have a specific name? I previously bought one that had the left-hand tap control water flow and right-hand tap control temperature. It didn't work well. My house is old and I don't want to do a major renovation to put in more contemporary shower controls.

when taking a shower, the lever that points down will not stay down; it raises be itself, thereby causing the tub to start filling up. I've checked the linkage behind the plate and nothing seems to be broken or missing. the unit was installed in the vinyl tub/shower in 1986 (a Delta brand).
what is the problem? thank you, gene rowland