Partially signed and multisig transactions within bitcoind go through
the raw transaction API, which does absolutely nothing if the sig
pushes the TX to a higher fee level.

Well, we'll have to make sure this is carefully and loudly documented in the new developer part of the website that's being worked on. Because this seems like a recipe for people writing flaky apps. In practice it would seem like you need to implement the fee loop in your own app:

1) Create tx with an estimated fee level

2) Add signatures

3) Submit. If REJECT for too low fees, increment, go to 1 and try again.