It would seem the safest bet in the long term is to go bigger on the speaker
Mmh, no - the safest is to take your power amp to a tech for a checkup before anything else.
Repeated problem as you described without explicitly stating that you have indeed driven them to smoke, indicates a possibility of permanent DC offset on the amp output.
DC offset you cannot hear, but you can see it.
Power up the power amp without any signal on the input (say, preamp disconnected).
If the speaker cones push out (or suck-in) and stay in the in/out position or very slowly move in/out, that is the evidence of DC offset.
If the amp gets a clean bill of health, well then, you are over-driving the speakers.
Reasonable pre-amp "pop" is not going to cook the speakers. Of course if the pop blows your hair back, that would be a bit of a concern.