John,
If the cable(s ?) are getting hot, it most likely is too small of a cable, a bad connection on the cable, or less likely, a fault in the starter that is causing it to draw too much current or a poor battery. I know you said all connections are clean, but, sometimes the crimp is bad and you can't tell. Also, woven ground straps can cause a lot of resistance. Cables should be #00 cable as a minimum, don't use cables designed for 12V, they are not heavy enough. What is the voltage at the battery when cranking. It should be at least 4.8v. Check next at the starter, it should be close to the same. If not, start checking voltages and work your way back to the battery checking at each connection. If you get an increase at one connection, it is either that connection or the one before it, depending on which side of the connection you put your voltmeter on, or that cable. Check both - and + circuits. Ground cable connections are notorious for being bad. If you have not taken it apart and cleaned it, don't count on it being a good connection.
The Pierce-Arrow Society website tells me you are a current PAS member, so, if you are looking for Pierce-Arrow Society members near you, go to the PAS website under member pages and go to the Member Roster. In the search function enter CO in the state and you will get two pages of CO members. I saw one other listed in Longmont.
You can also do a technical search under Publications in the Members Area of the PAS site for articles on starter problems.
You might also post this on the PAS website Message Board. I think more of the PA gurus check that page. The Parts and Services Directory on the PAS site should list some vendors that rebuild starters.
Good luck. Let us know how this turns out
Dave