95 Nissan 300ZX Automatic suddenly has shifting problems

This is a 2+2, not twin turbo, with 122k miles. A few months ago it started not quite making it to the next gear while accelerating. It's worse at higher speeds. It makes a vague rmmm and you can feel that it's not hitting the gear as the rpm gage suddenly goes very high. I back off the gas and gently back on again and it will catch on the 2nd or 3rd try.

Perhaps unrelated, I've had periodic charging issues and several batteries in the 7 years I've owned it. I just replaced a battery with one cell dead and the shifting problem is clearly better, but clearly still there.

I have, only on 2 occasions, smelled gas. Extraneous perhaps, but I just had the fuel filter replaced thinking it might be related to the shifting.

The last transmission flush was at 64k...yikes. I'm told not to do that yet as I may end up getting some other service that includes it. It appears certainly overdue in any case.

At 103k, had the timing belt, seals, water pump, thermostat, belts, brakes done. I've kept up with oil changes.

How can I figure out what's actually causing the shifting problem? I'm scared to keep paying for things I don't need without fixing the problem and I know nothing about cars! (Except that 300ZX rocks!)

Thanks in advance for any guidance!