Can I charge my iPad and use a 30-pin accessory at the same time?

The cableJive dockStubz may do the trick. Designed to extend the port in bulky cases, it features a MicroUSB port on the side to charge with older accessories that don't support charging.

MicroUSB should also support an iPad charge, though it may be very slow. See here for someone saying they can charge their iPad with a MicroUSB adapter (admittedly officially supplied by Apple, but the point is the protocol and cable can handle it). Worst case it will say "not charging" and will charge in sleep, and when not charging the drain will at least be significantly slowed. You will probably need to plug the microUSB adapter into a high power USB port – ideally the iPad 10W charger itself.

I can't guarantee this would work but, were I in your situation, I'd give it a shot and let us know. You could always return the adapter if it didn't suit your needs.

Good luck!