The reverse, relatively speaking could happen, as well, with the Dems in 2020+ getting four seats from the same resignations/deaths. The right is far more likely to see irrational pushes like upping the court number.
The answer to senators voting themselves out of office is to simply make existing members exempt. That's typically how the legislation has been drafted in the past, at least.I don't think term limits would solve much, you would cure some problems yes, but create new ones, such as even greater power of lobbyists. Anyway, Senators are not going to vote themselves out of office.
You are entirely correct about the power of lobbyists growing.