Let mne reply to my own topic.
I finally figured out the problem. The Rigblaster P&P only forwards audio when RTS is high (PTT light on the P&P comes on).
HRD uses CAT PTT so never raises RTS. In the radio config you can set RTS, but then it's always high (=always TX).
The workaround for now is not to use HRD, just DM780. In DM780 you can configure it to use com port PTT.
Very surpising that this very common combination does not work well