Hello !
I think you have in your town, or near it, a shop selling industrial parts (hydraulic hoses, bearings, bolts, etc... for the agricultural or industrial sector).
Go see them and ask for a suitable grease for lubricating splines (high pressure, difficult access, high temperature). I bet they will offer you suitable lubricants in sizes ranging from the small tube to the 200 l drum. And at a price so low, you'll want to buy all the shop.
These application are very numerous in agricultural or industrial machinery. So maintaining these machines is widespread.
And of course, can't be too expensive because industrial people tend to look at the best offer every time.
Just my 2 ¢...