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The ole 308 shouldn't have to much trouble holding second with the 4:44 gears im thinking should be quite easy ??I did an LS swap into a VC a while ago as a burnout car, stock engine, just a tune and it had no trouble spinning 205/65R15's on the 3.08 diff through a 4L60E. Had a 308 with VT injection in it before and the trimatic struggled to hold second. If you don't have torque, change the gearing.
You can pull 3rd easily with 4.44's. Wouldn't be a hell of a lot of tyre speed in 2nd, more smoke with a faster tyre speed, and they won't squeal.
Another thing to look at is the oiling mod on the 308, sustained high revs can starve the cam and crank of oil due to the crappy draining of the oil in the 308's. The basic mod is to flow the pump and drill a hole into the #1 cam journal to allow oil directly into the bearing rather than being fed along the galleries. Look it up, there are a few different mods, some simple, some complex.
I would say drill the back of the heads and fit dash6 lines down to sump (above the dipstick)One recent mod I have been told about with the oiling system on these is to fit a -6 or-8 fitting into the sump, near the oil dup stick....Run a line from there to a catch can.
Another one is get restricted push rods...ie, the oil feed hole in the pushrods need to be smaller in diametre......Also the cam retaining bolt has a hole in it, which should be sealed up, then have that cam oil hole drilled.....
So a few more ideas for the Op to research