DISCLAIMER: I be newb.
Fuel pump problems, in my experience (which is quite limited) seemed to involve working fine until it got revved to a certain point, and then the car would hesitate and eventually just died. It wasn't gear related. Have to tried accelerating fast in 1st or second ?
The ICA controls the idle (again, to the best of knowledge) and when mine died many years ago the symptoms were that the idle would not hold. I could start it up, the engine would rev up, then drop and die. I could keep the car going by keeping a foot on the accelerator when in N. So, I would doubt its the IAC.
The IMRC should be easy to test by unplugging the IMRC, but a malfunctioning IMRC does not sound like the culprit.
You could clean the MAF and try that. Does the car show any codes ? What about the exhaust ? Clogged cats ?
Mad Dog