My gut tells me somehow we get a backup center and Payton Pritchard ends up on the Jazz by July 18.
My feeling is also that if we were to use the TPE, it would be as part of a trade to flip someone already in the rotation for someone who either fits better or fills a bigger need, where the net increase in payroll and tax would be marginal. So yes PP would be the most at risk since he would probably fall out of the active rotation anyway. But he's also cheap right now, his salary profile and skill profile fits the bill of someone as an insurance player. The other person might be White, if they think that Brogdon's injury history is worth punting on. His salary is a big enough chunk to bring back someone meaningful without having to blow the whole TPE. Other than that I don't see who else we would trade out in our active rotation.
I still think the most likely outcome is that they let it expire, which would mean they're happy with the team as it stands, and get a vet min guy as a third big. Could even be considered 4th big, depending on how Gallo can be classified.