I was leaning towards c), but wasn't sure.
The procedure for the Philipinnes is not the standard ICAO. It is the same as FAA:
each pilot shall continue the flight according to the following:
(2) Altitude. At the highest of the following altitudes or flight levels for the route segment being flown:
(i) The altitude or flight level assigned in the last ATC clearance received;
(ii) The minimum altitude (converted, if appropriate, to minimum flight level as prescribed in §91.121(c)) for IFR operations; or
(iii) The altitude or flight level ATC has advised may be expected in a further clearance.
Therefore, in the scenario given the correct answer is to maintain the assigned level, or minimum IFR altitude if higher.
Also, as a follow-up question. Since HF is notoriously unreliable, how do you deal with no contact? Under what circumstances would you initiate a full-blown lost comm procedure?
Good question but I would say it is something of a moot point. You will be trying to establish comms by all available means. You will either establish comms before you reach a point where you need to make a level or course change - in which case you will continue in accordance with lost comms procedure - or you'll get comms back before that happens.