Dave, it's time for the mech to come out of the cabinet. It is way too filthy tho clean effectively with piecemeal approach. The cams, bearings and microswitches will have a better shot at revival if they get thoroughly clean.
Before removing the whole mech, first try removing the magazine motor so that you can manually rotate the magazine and get the records out. ALL motors must be removed anyway for proper cleaning.
The method I outlined using floor stripper was SOP for the industry down on Tenth ave (coin-op district). it is much cheaper them specialized products and the only warnings here are that it can etch soft metals like aluminum or glass if used full strength and not rinsed promptly. Whatever chemicals you use, watch out for the record numbers on the magazine. It is best to remove the magazine and wash it separately and test how the slot numbers deal with the chems you use.
Everything should to come out of the cabinet and be washed. Use care in washing the amp and power supply and try to keep most water out of the transformers. Blow everything dry as I mentioned previously.
Washed machines are much more pleasant and a lot of little problems go down the drain in the process. I wouldn't want some old barroom's gunk in my place either.
Rob