Java_avaJ I do exactly this every morning, 2 cappuccinos which I make one after the other and if anything I actually find the 2nd is the faster from time to time.
I’ve tried distribution without tamping and could never get properly pressurised shots, always coming up very short. I grind, distribute, tamp, pull. For the second I do a quick wash of the PF, run a bit of water through the group head to get rid of leftover grounds and repeat the process for prep of shot 1.
Have you tried the 2 with tamping too?