I too have loaded the 130gr TTSX in .308 but not the 06. Ive checked the data for 30-06 a while back and Barnes bullets build pressure differently than standard cup and core designs. According to the Barnes data nothing is really gained between the 30-06 and the .308 with their 130s.
Ive loaded a bunch of the 125gr hornady SSTs in
308 also. Mainly reduced loads for the young uns. They expand violently even at reduced velocity and sure do a number on Southern white tails. They dont seem to exit though instead fragmenting and the core almost always seperates from the jacket.last one i only recovered 69gr of fragments total after the shot.
Im running them about 2200-2400fps. The 125gr Accubonds hold together better and should do well at -06 velocitys
Ive tried factory 125gr core locs in 30-06 years ago and they didnt shoot for beans with about 8" groups. Never tried handloading 125s for that rifle, and stuck with tried and true pet load with 165gr bullets that shoot true 1/2 minute from my 116 and a Burris with ballistic plex reticle.
If i was going to shoot something that light and fast in -06 Id personally chose the Accubond.
Nosler is showing 3300+ with several different powders including RL15 and 3400+ with Varget
Good luck