I don't like to put "sticky stuff" on pto shafts, it's just a dirt collector and that makes them wear out faster.
EVERY time I put a pto powered tool on my tractor, I spray the shaft with wd40 or similar product on the shaft and wipe it off to clean it. Then I spray it again to make it slide together easier. I also spray the pto and locking coupler.
IF it stays on the tractor and get used, it's moving all the time and won't get stuck. IF it sits, I pull the shaft off to keep it from sticking.
SR
Im supprised the clutch is still in good shape. was dangling the whole 800lbs trencher by a chain through the U joint on the clutch. Glad its good as its a funky non-standard keyed connection I cant find anywhere. Had to get a new PTO shaft anyway as the OEM onw was way to short. Cheaper to get a new shaft then pop the U-joint one end off & replace it with the clutch than get parts to lengthen the OEM one.To the original question, a quality anti seize is going to be your best option, I've used used a good brake caliper grease in a pinch and it works well but preference is anti seize.
Either silver or copper will work for ya.
I know your pain, I had to remove a shaft from a tiller last year, ended up having to destroy it because it was not going to come off in one piece.
Bradco wants & $1k for the PTO shaft & clutch assembly. As best I can tell my existing one is the same length as the OEM one... Each half shaft is 6-8" long. They are inches from even touching when installed even without the Quick Hitch. So even the OEM solution wouldn't have helped. No clue what tractor could work with a PTO shaft that short.I was lucky, the tiller used a std. 6 x1 3/8 spline, the clutch was shot and not worth rebuilding anyways and ended up being cheaper to just get a new shaft/clutch assembly from agri supply.