Since you have the tank down, you might as well replace the pump. Also Its a good idea to change your fuel filter at the same time, and since its so cheap, buy a new relay as well. With those three things you can totally eliminate the fuel pump as an issue. The only other possibilities are a bad FPR, or a pinched fuel line. Since its load/heat related, I'm leaning more towards fuel pump. I doubt you have a pinched fuel line, but just visually check it under the hood connected to the fuel rail. I'm thinking a bad FPR (or missing/cracked vacuum line) would raise pressure, not lower it, I suppose anything is possible though.
I'm having fuel pump issues of my own right now, but I'm confident a new pump, filter, and relay will fix yours.