If $3000 is in the ballpark of what you're willing to pay, then the ~$700 premium to secure a P fare is reasonable, IMO. I suspect there may not be R inventory currently available on the desired flights, so the premium for P fare is essentially insurance to guarantee the upgrade as it may not clear in peak season.

For what it's worth, the P fare roundtrip from TPA (if that's home) will net about 18.5k PQM, 9250 more than an upgraded coach fare, and even a small amount of travel over the rest of the year would secure at least Silver or one tier higher than Mom would have otherwise qualified for. There's at least some benefit to that.