goatpig,
The bug we are running into looks a lot like the problem reported on bitcoin github titled "signrawtransaction unable to sign p2sh-segwit multisig transaction"
here: https://github.com/bitcoin/bitcoin/issues/12418

I think sipa's answers, including the code fix he provides towards the end,  may give a clue to where in Armory code the bug is and how to fix it.
Maybe the solution should be the 'Ugly Workaround' provided in the github issue above?

Could you please point me to the Armory code file where Armory signs multisigs? Perhaps I'll be able to lend a hand there.

Hope this helps.