About 180 times per second is what I would like.
Yes this is still very slow for a processor.
What is the difference between P-Channel and N-Channel?
Google it but basically P-channels pull up and n-channels pull down.
What is a drive transistor?
A transistor that is used to drive a load. Drive:- to power or to control.
Can shift registers work fast enough for the 24 transistors?
180 time a second for 24 outputs gives you 4320 pulses per second. So this is 231uS, one instruction on the processor takes about 0.625 uS (yes I know about it doesn't always) so that gives you in the order of 300 instructions executed for each output. What else do you want to do that is taking time? Without this information we can't tell if you have enough but I suspect you do.