Are you sure you don't have that backwards? I've owned an F2 (which honda made from '91-'94) and an F3 ('95-'98), and the F2 had the gravity feed set-up, while the newer F3 was the one with the fuel pump--because of the extra fuel flow demands for the ram air.
I've known any number of racers who installed the ram air set-up and carbs from an F3 onto an F2, and the fuel pump from the F3 had to be included in order to avoid exactly the problem you're experiencing.
Apparently, you've gotten the fuel petcock to work--the difference is that the gravity feed F2 petcock is vacuum activated, while the fuel-pump-fitted F3's was not. The simple solution was just to route the vacuum line from the F2 petcock to one of the vacuum ports on the intakes of the F3 motor. (which is exactly the stock set-up on the F2. there's a {capped} vacuum port on each of the 4 intakes, which are there to allow for a vacuum meter when synchronizing carbs--on the F3, all 4 are capped off, on the F2, 3 are capped and the 4th takes the petcock vacuum line)
Anyway, you need to get an F3 fuel pump and install that on your '94 if you want that '98 motor to be all that it can be. :waytogo: