[PAR_WIG1350]

Full disclosure: I haven't personally worked with air cannons, but I have a basic understanding of the physics behind them.

For the restricted tank opening, you could precharge a smaller, separate volume outside of the tank from the 1/2" NPT port and have a larger outlet from that volume to the firing valve. It might even be beneficial to further reduce the size of the opening between the main tank and the precharge tank to allow for a smaller, and possibly less expensive, valve between them. If you reduce it far enough, you might not need a valve there, but it might slow down your firing rate.

For calculating the effects of barrel length, I recommend testing a few different lengths and fitting a curve to the result.