I'm kind of leaning more towards just remove the pump and take it in to CAT for servicing, if they will even do that for me?
Take some Vaseline with you........
Remember their labour will be north of $150/hr and unless you agree to let them install the "repaired" pump then there would very probably be no warranty on the repair IMO.
They might try to talk you into purchasing a Remanufactured (Reman) pump assembly.
FYI the 289-6340 Pump Gp is now updated (through a couple of iterations) to 398-7470. The Reman for that P/N is 20R-7877 but I don't know whether or not any Part Number earlier than that would be an acceptable Core Return for a Reman pump. If it is not then you end up buying a new pump - $$$$$$$$.
Aftermarket pumps seem to be available. Reman 20R7877 around $4000, new 289-6340 about $4500.