So far, I've thought of using 2 old 20 oz CO2 cylinders I have to store air. That gives a good amount of volume, plenty for up to 5? good powered shots. These would reside in a backpack along with a couple homemade pumps modeled after the ones used with old airguns. One pump would have a bigger bore to charge the tank to 100 to 150 psi. The next would take it from that to 200 to 250 psi. The last would take it to the 400 psi I want. You might even be able to get by with 2 pumps. Each shot would get progressively weaker, but with a chronograph you can get a good idea of how many acceptable shots you can take before needing to top off the tanks.
The other idea is to build easily detachable air cylinders that hold one air charge each. Take a shot, swap cylinders. The big problem with these is the cost. Each one would run about $10 a piece.
Switching from a dump piston valve to a poppet / hammer valve could potentially give me better ability to get more shots per fill with either system. However, to get the power I need out of those valves, I'd likely have to switch to higher pressure air than what I'm using now.
Right now, I'm looking at the first system as being the most feasible. I'm planning on modifying my shop compressor a bit to see if I can get it to bypass it's built in tanks to pressurize my own aluminum CO2 cylinders up to 200 or 300 psi. My shock pump can get it up to 400 after that. I know from preliminary chrony testing that 300 psi produces a powerful shot, so I should be able to shoot until my tanks are down to that pressure. Once I get to that point, a hundred to 200 strokes with the shock pump should get my to 400 psi again. I've got to do a little math to see if it will work for 5 good shots. If so, I think this is the route I will take.