@lgaetz and @billsimon, thank you both for taking time to respond.
Unfortunately, there is no documented list of strings that Medicare’s IVR might require. And, that’s only one of the many IVR’s that our billers call on a daily basis. (It’s just the specific example that has an open ticket on my desk. 
)
I’m guessing from the responses so far that there is no way to tell FreePBX/Asterisk to stop listening for feature code strings during an active call. Or, it’s definitely not a widely known capability.
Either way, that’s a major bummer.
Guess I’ll look through the source code to see if I can find a solution.