Well, I don't particularly enjoy hunting birds that behave that way, so if I thought there was a decent chance of finding a more cooperative bird somewhere else, I would most likely give that a shot. However, since we are talking about this specific bird, this is what I would most likely do:
First of all, I would probably try to roost the birds in the evening. I would go to the oak ridge above the slope, get inconspicuous somewhere in the vicinity of where I thought the birds were likely to roost, and wait and listen until dark. Since this bird isn't chatty and apparently has an aversion to calls, I might just offer an occasional soft cluck, maybe rake the ground litter like a feeding turkey once in a while, but otherwise just sit quietly and hope that I either hear an unexpected gobble, or hear turkeys fly up into the trees.
If I was to get lucky and hear the birds at dark, then I would know exactly where I am headed the next morning before daylight. I would get upslope of them in the dark, as close as I dare, to the northwest (since they have moved either north or west the other three days). If I didn't know where the birds were, I would take my best guess and be northwest of that spot, once again upslope of my best guess. I would hope that the gobbler would let me know where he was early enough for me to move in on him in the dark. If he did, I would move deliberately, and set up, once again, as close as I dare, upslope and to the northwest. I would not utter a peep, and I would wait until they came out of the trees and hope they came my way. If they bi-passed me somehow, I would try to negotiate back around in front of them before they got off the property. As a last ditch effort, I would throw the whole turkey vocabulary at them and hope something stuck. If not, I'm off to another location.
On the other hand, if at daylight I don't know where the gobbler is on the roost and he does not gobble early enough for me to move in on him, I would stay back, up on the oak ridge, and again to the northwest. I would hope that either he or the hens would make enough noise to let me know where they were headed, and I would try to get in front of them as the moved from the roost. If not, I would just hang out, maybe sticking a decoy (oh, noooo) in the ground while I waited. If they did not show, I would eventually start calling,....first conservatively, then aggressively.
If, after that, I felt it was hopeless, I would either call it a spring....or head for another spot and hope for a last-minute miracle bird to end the season.