Sounds like it not transferring the weght
Does the front suspension lift much ?
what shocks ?
do you have a sway bar on the front ?
disclaimer;
with CalTracs they live a free movement like 3"-6" inches
like 5" in. of travel before the front wheels leave the ground,
is what they say/recommend IIRC
My last 68 RR liked only 3.5" of suspension travel
with CalTracs stock springs & a 315/15 {a bunch of sidewall} M/T DR
if you have a big sway bar on the front
it will limit it from rising, loosen them or unhook them,
will help
IMO it's probably not transferring the weight,
you need to get traction, typical of OEM style stock suspension,
especially with a OE style rear leaf too, front sway bar,
shocks made to dampen, more than extend etc.
limited body roll from side to side, is what they are trying to do,
not transfer weight to the rear tire, from the factory
adj. shocks {both ends}, freeing up the extension front
& compression on the rears or
like an ol' 90-10 drag front shock will help too
tire press. can make a world of a difference too
air up the fronts/less resistance & figure out what the rears need,
to actually hook
Drag radials can be finicky, I've never used the ones you have,
mine {M/T} worked best @ 16psi - 21psi depending on track & temps
an adj. pinion snuber may help some,
but you still need a good weight transfer
Also maybe;
Try, don't do a big smokey burnout,
just spin them to clean them & get a bit of heat...
IMO sometime it softens the tire too much doing a
"big showy burnout" balls/wads up the rubber under it
& then they just spin
you may need to add ballast in the rear of the trunk too
these cars from the factory aren't meant to transfer the weight,
like you need them to, to actually get them with any power at all,
to actually hook well
good luck