Does it have to be a springer? A bullpup could be done with an air gun where a tube connecting the air tank to the barrel goes back to the stock behind a clip.
No. I think that an Eyes of Fire-esque regulator system would work like a charm, a precharged tank in the foregrip, and a dual-regulator output, and on firing, a Magstrike valve opens, releasing a burst of air that fires the dart. As the dart fires, some of the gas is siphoned back thru a tube hooked to a hole in the barrel and opens the breech thru a piston-tube that has a very weak extension spring that shuts it after the pressure is released by a hole in the piston tube. It is like an AR15 action, but with valves and air instead of firing pins and gunpowder.
Halfway, the gun would be more compact, easier to use, and lighter. And if done right, can kick a Magstrike's ass.