Sorry guys, I'm just finding this one.
The PWM controller won't increase output. It slows down the pump to decrease the amount of heat generated and to reduce wear. The only thing that is going to increase pump performance is to increase the input voltage.
The Gen5 LS3 pump was used on James Shipka's OLC with the Katech LS7 was a nice match for that setup. It made about 630hp. The pump had a small safety margin in that car but it supplies 14 volts at the controller input. That helps pump performance. Engine efficiencies and input voltages can make a big difference here as well since it's getting close to the maximum output of the pump.
It is normal that pressure will drop in a non-manifold referenced system during part throttle. The C5 Corvette fuel filter/regulator does the same thing and has very similar output curves. As more fuel flows to the engine, the pressure drop will increase to the point where no more fuel is bypassed by the regulator. There is another pressure regulator available that does not have as much pressure reduction, Delphi FP10075. It does have a slightly higher it-idle pressure of 61-62psi but will only lose about 3psi at full bypass.
Three things come to mind here:
One, the fuel pressure regulator may be partially dislodged and causing an internal leak. To check for this fuel module removal is required.
Two, there may be a restriction in the fuel line. To check for this a fuel pressure gauge would need to be placed near the fuel module outlet and compared to the pressure at the injector inlet. A small difference will be normal as there are losses due to friction and fitting restrictions.
Three, the pump may be too small. At 50psi the regulator should be sending all of the fuel to the engine. At 50psi/13.5v the pump can supply 326 #/hr, enough to feed a naturally aspirated engine to 652 horsepower at a conservative 0.5bsfc with an appropriate injector. However, there's not much safety margin.
Some numbers:
At 13.5v:
60psi = 300#/hr or 189 liters/hr
55psi = 313 197
50psi = 326 206
45psi = 339 214
40psi = 353 223
For naturally aspirated engines the brake specific fuel consumption (bsfc) is considered to be 1/2# per hour of fuel for each horsepower. So, at 50psi the pump can provide 326#/hr. Divide this by 0.5 (1/2). That results in 652hp. However, there's no safety margin.
You may also want to check here for some injector calculations
http://www.rceng.com/technical.aspx
For 650hp, 80% injector duty cycle, and 58psi fuel pressure a 44 lb/hr injector would be a good choice. It sounds like you may already be at the limits of your current injector as well, but the fuel pressure side of things should be fixed first.
Injectors are typically rated for 43psi (3bar), not 58psi (4bar). I won't go into the gory details of all this unless you want me to, but it's a good practice for us. So, at 42psi you're looking at a 52 lb/hr injector (assuming eight injectors.)
You may also want to check that the wire gauge to the relay(s) is 14ga minimum and that there is not a large voltage drop to the relay output. The Gen5 LS3 pump needs 12 amps.
If it is determined that the fuel pump needs to go bigger the easiest thing to do would be to put in a ZL1 fuel module. You can test this by putting in the fuel module using the 58psi regulator that is in your current fuel module. Though not recommended for extended use, it will work to get the system figured out. The ZL1 is capable of:
60psi = 391#/hr = 247 l/hr
55psi = 415 262
50psi = 436 275
It also needs 17 amps, so a PWM system is recommended for this setup for long-term use.