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2000 Honda Accord Runs rough and hates the heat

I’m in desperate need of help with this, so I’d appreciate ANY ideas.
I have a 2000 Honda Accord LX V6 auto with about 125k on it.
It seems to me that when I’m going downhill for example - so I am not giving it gas - it feels like its running rough - sort of. It kind of feels like the brakes are being applied then released, applied then released.
Now, once summer arrived and I had to start using the AC all the time, after the car was warmed up and having run for 20+ minutes, it would REALLY start running rough. I watch the tachometer and it bounces up and down. When I turn off the car for awhile like to go in to the grocery store, when I come out and try to start it, it wont. It just cranks but wont catch. If I do manage to get it to catch, it stalls. I have managed to get it to catch-apply the gas and pop it in to drive and make it home, but something is obviously very wrong and I dont want to get stuck somewhere.
I have a code reader and the car has not produced any codes.
Any ideas? Please help!

do you have an automatic transmission?

if it’s automatic, i’ve experienced the same effects when a transmission brake band is dragging on a gear drum, for example if you’ve got a kickdown band and a reverse and low band, if the kickdown band is to tight it could be grabbing when it shouldn’t, but it seems kind of unlikely that this is the case, has it done this before?

yes its an automatic. i could be imagining it, but it seems to begin occurring when my fuel tank hits half-full. If i top off the tank, the problem goes away.
Thank You for responding! I really appreciate it!

You’ve replaced the fuel filter, I take it? Even tho a bad filter doesn’t cause a car to stall only on a half full tank but it is easily and cheaply replaced.

I’d check your fuel pressure. Fuel pumps are cooled by being immersed in gas. When the tank is lower, it cools less and the pump’s bearings start binding, causing the fuel pressure to drop intermittently.

IOW, I think your fuel pump is on its way out.