Puzzling fuel problem

[Jewelfae]

So i have a 2006 hatchback with 143k miles on her.
She's one of the super basic models.

I'm having issues keeping her running nicely and I can't figure out why. So here goes.

My car runs great until she doesn't. You will be driving along and all of a sudden she will just "hiccup". She will suddenly kick on the check engine light. She will run very roughly like she's low on gas. You can not accelerate at all she will do 10mph max flooring it makes no difference. This often happens at a stop but it's extra fun at 60.... The car doesn't immediately drop speed she coasts like you took your foot off the pedal.

To correct this 99% off the time its stupid. You turn my car off count to 3 turn her back on. She's good. Occasionally you need to try a few times. You don't need to pump the gas or do anything at all. Just off and back on and she will run perfect again.

The check engine light goes off after 4 starts.
I had it checked after an instance and it gave me a throttle body error.

So we replaced her throttle body : no difference.
I've added heet to the gas tank: no difference
I've changed the fuse to the fuel pump: no difference
I've given her a new battery: no difference
I've installed a new exhaust system: no difference
I pulled her ac fuse because it seems to happen more often with the ac on and my dad thought her ac pump was failing and putting to much load on my engine so we disabled her ac by removing the fuse: no difference.

It doesn't seem like the pump itself I shouldn't get immediate correction turning it off then right back on.
We don't believe it's the fuel filter for the same reason.
It doesn't seem to be an object in the tank because this happens with the tank totally full. I've also run the tank to nearly empty and had her drive like an Angel.

She's still getting 30+ mpg freeway.
This issue can happen several times a day or it can happen once a month. There is no pattern nothing we can say always triggers it.

I'm at wits end. I can't spend money chasing this problem. I have 4 kids in car seats so it's not worth having a mechanic tear her apart for thousands to try find this problem but my dad is mechanically inclined as is my partner shop if we could get an idea what to fix we might be able to within the budget I can afford to sink into her.


I'll take any guesses you have that I could test.