Drive Fight on 7400 Series
Possible solution: instead of having one R1 per driving transistor, put R1 on the output of each shift register. Then the maximum current that can flow between two shift registers is limited by 2x 47k resistors, but the drive path between shift register and transistor is the same.

(I'm not sure if the 10ns shoot-through would actually be a problem, but given the amount of discrete logic it's worth considering what happens if part of it fails and two shift registers get stuck on)