My shower diverter valve has gotten all gunked up due to the very high mineral content of our water, to the point where it won’t turn unless you put all your weight into it, and I’m trying to fix it because a) my wife can’t turn it, and b) I’m worried that it’s going to break.

I am hoping that it’s a simple cartridge replacement, but I can’t identify the manufacturer and model. It doesn’t help that the rest of the shower (main handle, shower head, and hand-held shower head — the diverter switches between those two) are several different brands (American Standard, Grohe) but none of the pictures of diverter valves made by those brands look like mine.

Here are pictures:

Handle (on stem, and back view)

Escutcheon and handle mounting nut (Handle locks into groove on nut, which has adjustable depth by turning)

Valve stem itself is splined all the way down and has an E-clip near the end, but the e-clip doesn’t seem to actually be holding anything in place

(I suspect that the e-clip acts as a stop for the depth adjustment of the handle, but I am not totally sure.)

I suspect that the visible hex “nut” (which actually goes way back and flares out — just visible in the picture) is the valve packing nut, and that I should be able to remove it, but I can’t get it to turn and I have no idea where the threads would be.

Any ideas?

Alternatively, any way to remove the mineral scale inside the valve without taking it apart?