i'm guesstimating that the OP is questioning the procedure if necessity to significantly change FL while lost comms ??
I think adhering to the issued clearance is more important than providing a smooth ride.
The OP specifically stated CAT, not CBs.
I would maneuver as necessary for CBs but immediately return to the cleared route.
If fuel endurance became an issue, obviating a climb, then I would invoke the PICs emergency authority (he may deviate from any regulation or clearance ONLY to the extent necessary to deal with the emergency).
Just my honest opinion (and that's all it is: opinion).