How many military pilots do you think have a current type rating on the 737? The C-40 pilots could probably transition quickly but there's only 28 C-40s in the US fleet so probably not enough pilots to make a realistic difference.

This isn't just a case of paperwork, either. A pilot can't safely operate a completely different type without training. Even if you expedite it, it's likely that resolving the industrial action will take less time.