Does anyone have a reference for the AIP or Jepps for the procedures to be used during an HF outage
Basically ... failure to maintain comms is the same as a comms failure ... so follow the procedures as per ERSA EMERG.
Continuing a flight when HF comms cannot be established before leaving VHF coverage, and proceeding knowing you may not be able to maintain normal comms and report an emergency is a pilot decision.
ATC will declare a SAR phase based on missed position reports, and assume you stay at last cleared level until comms re-established.