Paul,  I reached out to many a AFS people.  Looks like on the newer Pro 700 FW there is a toggle to set the radio port to "manual" on the 392.  That appears to stop the Port C reset on key cycle.

Toolbox->GPS  Set Correction Level to "other modem"

Toolbox->GPS scroll down using the middle scroll bar and on the very last page there should be Radio Port Setup.  There should be an option for "Manual"

Go into the RDI screen and configure Port C as you would on a 372.

I should credit TS79 for helping.  I didn't realize he was the one who asked the original question and got me the fix!