Which TransGo shift kit did you use?
the TF-2 street an strip kit or the full manual TF-3 kit?
if it's the -3 full manual kit, you can test 2nd and 3rd gear sitting still in the garage with the tires on the ground. the full manual kit is set-up so the trans is in whatever gear you choose.
with the engine idling, pump up the brakes good n tight and put the shifter into 2nd gear it should engage and drag the motor down some, and you can try revving the motor slightly to see if it's engaging the 2nd gear band.
you can also test the stall speed of the converter by pumping the brakes as tight as possible, putting the shifter in 3rd gear, and momentarily going full throttle, the converter will go to max stall speed for a second or two. don't hold it wide open more than a few seconds or you could damage the converter or high gear clutches. the TF-2 kit won't allow such shenanigans as it is set for auto shifting.
we use to do the high gear throttle test all the time to keep tabs on the health of my race converters. this test works because the trans in high gear doesn't have the torque multiplication of low gear to over come the brakes.
some tricks I used to use to not blow away skinny hard tires like you are stuck with in this class.
when running a three speed auto, was to over-cam the engine killing off some low end torque. (more duration than ideal)
running headers (short runners) designed for a stick car, with no/or very short collector extensions, to kill even more low end torque.
having used Holley 4bbls. in this scenario, I would use a 50cc accelerator pump on a vacuum secondary cab with small to medium shooter size to carry a long duration pump shot off the line and down the track to the point where rpm was high enough.
and on really slimy tracks in pre-concrete launch pad days, I would even start in second gear and run it as a 2 speed. this was all in the days before trans brakes, when I was doing 2000 rpm foot brake launches.
remember these are hard earned secrets, so don't share them;-)