The TP 1300 or equal by other mfg does allow the fan support hardware to be attached direct to framing. The TP 16511 type is a nail-on & 35# rated, and I know of no provisions to 'attach' any type of fan braces to that box.
I'm quite sure that some enterprising person could mount a 2x? over the top of the box & run lags/screws into that but ...bye, bye listing.
