The fuel pressure drop is a little higher than I would expect for 45 minutes. It makes a difference with a warm engine and hood down will maintain higher pressures; With hood open and a cool engine your pressure drop may be normal. With my car when engine running I get 55~56 lbs pressure. When engine is shut off pressure immediately drops to 51 lbs: After a hour it drops another 15lbs to 36 with a hot engine.

Needswings has a good price on accelerator pedal. I really think you should get a new pedal to, hopefully repair the hesitation at idle.

The P0435 code is a simple circuit to deal with as only three wires run between the pressure sensor in the fuel tank to the PTCM. However, it is a pain to get the plastic divider off the fuel tank to get to those wires. As M60Adriver suggested before trouble shooting that code you should get a new gas cap. The caps are double pressure relief as they allow both high pressure and vacuum to normalize through the cap. We are talking like 0.5 lbs. of pressure so it isn't much. So before messing with wiring I think it is best to first replace the accelerator pedal and the gas cap.

PS. You talked about the siren draining on your battery. You should at the minimum disconnect the siren at it's connection under the windshield cowl to stop that battery drain.