It sounds like the car only has issues when under a load. That could be a lot of things, and without the diagnostic equipment to see what's happening, you're kind of stuck shot-gunning parts and hoping you get lucky.
Normally I'd say it's probably spark plugs or plug wires, but you stated you previously replaced those. Of note though is you said after that it might have even gotten a little worse. Maybe one of the spark plug wires is not making a good connection?
A MAF that doesn't read correctly could cause an issue under load, but again without having datastream data for the MAF, it's just a guess. Fuel pressure could be another cause, but I think you previously said you changed the fuel pump and fuel filter as well, so that reduces the chances that's the issue.
Maybe you have an intake air tube with a crack in one of the accordion folds that opens when the engine shifts under load. Worth checking. Or maybe there is a brittle vacuum line or mis-routed vacuum hose that opens or gets pinched when the engine shifts.
-Rod