Just called Shimano tech support and spoke with Justin (great guy BTW). He said that the 7900 and 7970-RD use the same cage, but the assembly process is slightly different. He also said that the 7970 cages can still be ordered, they just don't have any instock in the US, but the total for both plates is $366. So I have 2 options:
1. Spend $366 on new cages
2. Take one of the 7900 rear dreailleurs I have in the basement at strip the cage from it.
I think I'll be going with option 2 and ordering a few 7900-RDs from Fleabay should this happen again.
DaleRider - Did you successfully swap the cage? Just curious.