Fuzzy logic and adaptive TCM programming can cause it to choke. Amsoil ATF would have similar shift quality to T-IV, as would most universal ATFs. Being a full synthetic, that would a good choice---- Amsoil ATF, and not ART.
The problem with lower(ATD) and non-HFM'd fluids(ART) is that the TCU programming could drop the line pressure to smooth out the shift. You don't want that to happen.
If you're unhappy with the shift speed, then maybe that fully rebuilt transmission isn't as 'fully' as you thought?
Check to see if there are any programmers that can address the transmission parameters. Even a factory dealer installed update might be better then what the vehicle shipped with.
You should also monitor transmission fluid temperature. It may be possible to acknowledge that 'someimes slips' with ATF temperature. If it slips when too cool, you need an ATF thermostat. If it slips when too hot, you need a big ATF cooler. Another option is to trick the ATF temp sensor by replacing or modding it with a resistor. Again, you'll need to know the temp/shift/PSI parameters to select the best resistor to trick the TCU to provide maximum PSI or shortest shift duration.
Find a shop that can modify the valve body for quicker shifts. A little more line pressure, a little less accumulation, a little more ATF flow through VB porting, can go a long way in speeding the shift.
How old is the T-IV? If it has more then 10k miles on it, its probably toast already. Flush it out and get an ATF UOA.
Excessive wear caused by excessive engine output, will be suspended in the ATF. That wear can mess up shifts. Toss some sand on a basketball court and see how the players react. Get a good fullflow ATF filter, like the permacool unit with a quality PH8A sized oil filter(pureone, amsoil, x2, napagold, stilko, trasko). The filter will keep the fluid free of particles that can get inbetween friction bands/clutches.