How to replace leaking tub/shower faucet stem

A very helpful support contact at Moen managed to put me in touch with someone at Amati Canada, who suggests that it is an "American Sole" unit. I can't find any information that suggests that's a manufacturer, or a line of products or anything -- so I can't corroborate, but at least I may be on the path to finding out who makes it.

Incidentally, in the meantime, I managed to find a workaround for repairing the part that was broken (I found a small plastic bit that sits firmly in the recess and can be screwed on, acting as a sort of bridge between the screw and the cap, so that when you turn the cap, it turns the handle again). It's not a perfect fix, but it's more than adequate for my needs. If I can get the part replaced, I may still, but it's nice to have options.

A few years ago I replaced the "guts" of my shower's faucet. It was about 10 years old and leaking, never quite shut all the way off. It is not hard at all. Just take off the knobs/face plates and there is usually a special tool that come with the replacement cartridge that allows you to yank the old one out. I probably yanked the old cartridge out with my own pliers but I can't remember. Point is you can do this for far less than $500 and its as easy as sliding the old cartridge out and the new one in. Since yours is 20 years old your biggest problem may be finding the make/model of the specific unit so that you can get the correct replacement cartridges for it.
A "rebuild" kit sounds like it comes with garbage you probably aren't going to need or can buy separately. A replacement cartridge is generally $23 and comes with all the o-rings you need.