I just used my super light slingshot, short, heavy latex tubing. Kicks like a mule. Because my regular, heavy, long slingshot system tubing needs to be replaced. Two things: looking down a longer device helps eyeball aiming and there's less deviation from recoil motion with a heavier device. For recoil you can resort to tensing up your body for the shot. Recoil control is a big part of accuracy.
Don't worry, my last post was double entendre mixing up car engines flow stuff. Actual gist of it is that there's a limit to benefit of speeding up the pressure fill behind the weight because there's a speed or timing of the weight boogying down the barrel and the objective is to choose how much you want to keep up with the motion of the weight down the barrel. There's also probably choked flow for a good part of the firing that might explain some linearity you found. Choked flow means you push harder but the air doesn't go any faster through the orifice (valve) but with higher reservoir pressure you stay in that max flow regime longer, hence more air buildup behind the weight. With a big valve you just get massive transfer and maximum pressure rise. It can be debated whether that is indeed the best circumstance. Most likely yes if your goal is absolute max power. Which you said isn't your goal. Part of your keeping up with the timing is the milliseconds response time of the solenoid. Good choice in my view.
There's a guy who made a supersonic air cannon. More hp! Rrrrruh Rrrruh Rrruh - Tim the tool man Taylor