The thing to do with telemarketers, I have learned, is not to immediately hang up.

No, it really is to hang up.

I prefer this to simply hanging up because doing the latter always makes me feel bad for several minutes afterward for having been rude to somebody who is, after all, trying to make a living.

Your emotions seem to be doing both you and the telemarketers a disservice - perhaps due to an instinctive misunderstanding of what kind of social transaction is taking place. The telemarketer is not socially vulnerable and nor are you in a position where perception will have future consequences. They also don't WANT to have an extended positive interaction that has no chance of success. Wasting five minutes on a mark that has no chance of giving a commission is strictly worse than an instant hang up. Your instincts are right that they are "after all, just trying to make a living" and you are just getting in their way.

I'm not saying it is necessarily worth retraining your emotional attachments in this case. You seem to attach pride to the act of wasting telemarketer time and guilt to the act of hanging up. This, combined with assertiveness practice you get and the cost of retraining yourself may mean that it is better to stay in the behavioral local minima.