They were like a fox in a hole. Simply minimize ground force exposure, drawing them out when possible, otherwise wait them out.
You can always dig out the old Roman methods of siege, i.e., burn them out from the air, etc., if you want to speed things up a bit.
They have already lost, it’s only a matter of time.
There is no sense at all to wasting lives in the process of clearing them out, seeing as how they have arrived at checkmate. They have no resupply, they have no navy, etc. The fat lady is singing at that point.
A comparison to a Roman siege is absurd. It wouldn’t have been the siege of an army it would have been the siege of an entire nation. In the meantime, as their population died from mass starvation and rampant disease, they would have continued work on their own atomic bomb.