I appreciated everyone's comments and wanted to follow up with what seems to be the answer.
My latest bulb has not burned out, and it has been 10+ months.
Apparently I'd simply had a streak of bad luck with the bulbs I'd bought.
My hypothesis that my usage or lack of usage of air conditioning in various seasons affected the electricity of the oven seems ...
Hums usually occur when the items or conductors you replaced or repaired are not remounted properly and vibrate while activated. Try checking out all of your connections and see if everything is mounted tight enough.
I'm surprised you've had this much response given the amount of information you've provided, like:
why is this a problem other than obviously miswired? How did you discover it?
Are they tripping for some reason?
Is your AC a 120 wall unit, or a 240 HVAC system (HVAC can be 120 or 240 depending on whether you have electric heating coils etc).
That said, i'...