Strake
Interesting situation.
I would try to revert to APP and report that 2 way communication had not been properly establised, then ask for further instructions.
If I was too near the final turn, I would turn final, continue the approach, reduce to minimum safe approach speed and make a blind transmission to TWR declaring this - if he was still talking to the other traffic I would contact APP. Given a 2-3 mile final it would probably be all sorted out and a landing clearance issued.
However, if no landing clearance was received by say 200', I would overshoot and keep trying to contact TWR or APP.
These actions would be driven by my need to mitigate risk. It is always arguable which is the best approach, but I'd prefer to avoid penetrating the deadside, as lots of things can be hidden against ground clutter and the scanning area is bigger and I'd resist orbiting on base as it is a chokepoint where other traffic could be following (e.g. non radio if permitted, radio failure etc.)
DFC
Thus one can never orbit in the circuit at an airfield without ATC i.e. AFISO, A/G
Am I reading you right here? AFISO and A/G cannot issue ATC clearances - although AFISO can issue taxi instructions to the runway holding point.