Exercises that go over joints is a good place to start, only if we agreed it will make my joints capable of taking more of this nastiness.
'More' of it, maybe... but a lot of joint locks and throws are able to cause damage even in strong healthy people -- that's one of the points of them, one of the things joint locks and throws are designed to do. As your partners get more experienced they should learn to be better at controlling you without injuring you.
If they go slower you'll have more time to realize something's wrong and tap out before you get injured. Like you said, when people are going fast sometimes the reaction times are too long to stop someone on time. It's probably good for them anyway, to have to go slow and figure out where the actual control and balance are.