About 8 months ago I removed what I believe is exactly as you've described: a metal framed sliding glass door from a cast iron bath tub with tile up the walls. (I then promptly destroyed the tile and tub, but that's irrelevant to this discussion...) There had been some holes drilled in the wall tiles, but the tub itself seemed to be fully intact. There was a lot of caulk everywhere that would need to be scraped off and then cleaned up with some sort of chemical. (I found a caulk remover from one of the big box stores that was fairly cheap, easy to use, and didn't do any damage to any acrylic tub so certainly cast iron and tile could handle it.) I'm guessing you also may end up with some holes in your tile where the door is secured that you may need to patch and/or cover with the new door.

You can install a small plastic or metal shut off valve between the shower nozzle and pipe to stop the water as shown in the link. Should be available at Lowe's, WalMart, etc. The water comes out of the shower head when you don't want it because the diverter valves on the newer spouts are smaller and that impedes water flow more and sends some of it up to the shower head even when it isn't selected. Here is a link that might be useful: Shower head shut off valve

The material was indeed Marlite. Thanks to those who identified it prior to removal. It was applied directly to the original wood slats, which are about 1" thick. There also no insulation along the outside wall, which we're going to fix as we go through the bathroom. We're going to do a subway tile surround with dark grey grout and keep the original cast-iron tub. Here are some photos after we removed the old Marlite backing.

i'm needing a rain shower and tub filler and would like all metal units. can anyone suggest some? i have Grohe faucets in most of the house and they seem to work for years without issue. not sure they make a simple shower unit with a metal shower head. would be fine without any wands as well. do they make units where everything is exterior to the wall as well? i would hate to have to rip up a tiled wall because of a failure of some unit inside the wall. thanks a bunch.