Frank,
When you mentioned the broken module bracket - that is what inspired me ask about the aircraft model - some earlier versions (not the S7) had a modified module bracket with both module grounds going through the bracket - S7 you should have both grounds going to separate screws on the intake manifold so that should be no factor.
It can be pretty perplexing to separate what is caused by fuel deals and what is caused by ignition things. I'll throw out a couple ideas; however, I think your diagnostic procedures so far seem to indicate a fuel deal.
1) DF 4's comments about proving the fuel flow are spot on. Based on your description, it sounds like the fuel pressure sensor is picking up at the split where the fuel goes to each side in separate hoses. Pulling the hose off at the carburetor and getting an actual fuel flow at that point for each side should determine if there is an issue between the fuel line split and the carburetor inlet.
2) As to the indicated fuel pressure under the conditions of the miss......if the gauge is right, the pressure is adequate. It is normal for the pressure to drop a small amount with increased fuel flow, but I believe the minimum fuel pressure Rotax specifices is a lot less than what you are registering. When doing fuel pressure ground checks, I use a direct reading automotive fuel presure indicator spliced into the fuel line at whatever point I want to check - not possible airborne.
3) On the fuel flow rate - again, if the gauge is right (my faith in gauges is rather low unless they have been currently calibrated against a direct measuring technique) Low fuel flow can be due to either interference with supply or low demand (less than full throttle or a prop that is way over pitched limiting RPM). If the flow rate actually does decrease to 3.4 gph...no way can the engine develop full power.
4) Again, DF4's comments about checking the carburetor, even though it has been rebuilt is a good call, likewise, a new fuel pump is not necessarily a good fuel pump.
5) If you get adequate static flow rate at the carburetor inlet - I'd be real suspicious about the carb or mechanical fuel pump.
Keep us all in the loop - the rest of us might find knowing what is going on useful.
Good luck,
DS