I got the same year/motor. Try to rule out the cheap/easy first. Wanting to die when you start accelerating but then responding almost sounds like a large breach in the integrity of the intake/vacuum. Like the motor thinks one thing based on maf input, but reality downstream is different. I would think anything causing that much hesitation would be throwing codes at you and you didn't mention any. Maybe clean the maf sensor. Verify the air filter isn't clogged up.
When my fuel pump when out, it just died, it didn't behave erratic based on demand, but I guess they could. Maybe check the fuel pressure at the rail. There is a schrader valve on the rail, will take you about two seconds. I think the numbers might fluctuate under load, so maybe have someone rev it up so you can check it under load and at idle. That would rule out fuel issue if you are pretty sure that's the prob. Fuel filter is kind of of easy to change. I don't remember the values. 35 at idle comes to mind, but verify that. I am sure there is a psi range listed on here somewhere that tells you what it should be.
Good Luck
Let us know what you find.