The teeth on this (at least 30-yr-old) shower valve on both the cartridge and handle are too worn to engage so I guess I need to replace both. I can't see any identifying info on the valve body so my inexperienced guess is that I should first remove the cartridge, take it to HD or Lowe's to find a replacement, then buy a new trim kit with handle that will fit the new cartridge and also have screw holes on the faceplate that will match both the 2.5" distance on the existing valve body and have some sort of barrel or offset to accomodate the fact that the tooth end of the valve is about 3" proud of the tile? Better way to do it? Anything else I am missing? Thanks.