I had a similar situation with my home CAA. Turns out they had lost the foreign request, so suggest that you don't wait too long before nudging them to respond to the FAA.
And yes, you will need a BFR.
And the guy above quoting 14 CFR Part 61.56(d)(1). is misleading in the context of this thread. That part states "A pilot proficiency check or practical test" counts as a BFR , not any new certificate issue. The question he was answering was an IR checkride so he was right but for a 61.75 certificate issue you need to get a BFR to use it.
You can use either a verified CASA medical or get an FAA medical by the way.