First, Thuney is gone. I don't know why we are even discussing this. If the Pats were going to keep him, they would be in discussions now with him. From every report I have seen, that doesn't seem to be the case. Once he hits the illegal tampering phase in a few days (if not now) he is likely to get a break the bank deal with another team.
Second, the Pats may have cap room, but they have a lot holes to fill beyond the o-line. If they trade for Jimmy Garoppolo, they will lose close to a third of their cap space without renegotiating with him. They need WRs and TEs and good WRs and TEs take up a lot of cap space. They need to fix the holes on the d-line and LBer. I don't see them paying Thuney top dollar as a priority.
Third, I don't see Thuney at center. He is a top guard in this league. Why would they pay him top dollar and try to move him to center? Do we even know he can properly snap the ball (see Damien Woody who was a great guard who went to center and could snap a shotgun snap for the life of him).