Can the R/T not be connected to the Interphone to allow direct comms?
Might be a regulatory/cost issue involved but in any event it's not been a possibility on any comms I've seen.
FWIW these days on many types (especially long haul) the communications with the medics on the ground will be done by the crew via satellite phone ( which in our case is part of the Flight Deck communications fit) rather than by using noisy, scratchy etc HF.