So the engine is apparently being fed such bad gas that it can't start easily and may be producing less power or misfiring?

That would imply you are pressing farther on the pedal, opening the throttle more to get the car to run - the computer will see this (I guess) as if you are pulling more of a load, or you are at high altitude. How else can it compensate for this other than delay the shifting?

SOunds to me like you already know what the issue is: Bad Gas.

Injector cleaner won't fix that - either burn the gas out of it by driving or drain the tank - then buy 'good' gas and see where it goes from there.
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Now, I have not had personal experience with "bad gas" in at least 30 years, but I DO hear about it from time to time.