I had the exact opposite problem with my MSD box I ran years ago. It would not spark while cranking, however, as soon as I would let go of the key, it would fire as long as the engine was cranking at a good pace. I also found that the original resistor wire, since the first gens did not use a ballast resistor, was starting to melt with the use of the box. I took the box off, and everything fired right up as usual. I believe your issue is a wiring one, but if MSD thinks its the pickup then try that first. I too wired my box exactly as MSD had on the diagram.

The more I think about this, the more it sounds like the box is wired for power only when cranking? If that makes any sense?