Im not following this logic...
a moderate to mildly loaded 7-08 shooting 150gr bullets will easily get 2600-2700 fps (more speed is possible if youre willing to go with a hot load.. but really isnt at all necessary)..
minimum impact velocity for ttsx is 1800 fps (although many will tell you that 2100 is really more optimal and reliable..)..
the same 7-08, 150gr load mentioned above that starts at +/- 2600 will still be cruising along at about 2150fps at 300 yards..
so unless the OP is planning on shooting PG with his 7-08 at distances of 300+, there should be zero concern in using the barnes..
FWIW, I shoot a 308 with 168gr barnes TTSX (exclusively.. I shoot no other loading in 308), that is about 2650fps at the muzzle.. Ive taken game out to about 225 with it, and shot targets beyond 300.. and never once had a performance problem from the bullet.. (taken everything from zebra and wildebeest
to whitetail and hogs with it over many, many years)..