Anyway

I too have experienced 5744 and seen what you saw. And almost gave away that first bottle after the first 5 shot string.
But then I copied down the chronograph readings. It's just possible the answer to this conundrum MIGHT could be crafted ALMOST immediately, if not sooner. Wait.... how can "sooner" come before "almost immediately"?

Uhhhh.... What brand of coffee do you favor? (please include your Pet Load information as to either weight or volume of grains... uh, grounds.... etc etc)
(I need a Smilie here that slaps itself) (of course, others MIGHT suggest that I need a Smilie that is slapped...... oops
ANYWAY.... I would suggest that 5744 is a perfect example for anyone who would suggest that some powders give excellently consistent pressure/velocities even when not individually weighed. It's a double base. They're usually more consistent in ignition I believe. So there appear to be powders that either won't vary the amount of unburned powder or somehow produce unvarying pressure/velocity if they do.
I've been experimenting with 5744 in a 40-65 since the middle 90s. I recently got a 40-70SS that kicked that same testing off again. Outside of the usual things we quest after, it amused me to see HOW LOW CAN WE GO...... with 5744. I figured to use the chrono to warn me that the load was getting too low. Predicted first shot velocity was verified before shooting a 2nd. Each shots velocity was noted for the same reason. Total variance (or extreme variance) was used as well. Temperature was considered up front (and back).
That powder, so far, appears to me to be a powder that would answer your question as: clean vs dirty doesn't matter.
I would actually shy away from trying to get most powders to shoot dirtier than what I'd identified as normal for them. And I think proving your question would require reloading in a way that would get the subject powder to be dirtier, as proving "really mattering" between two different powders seems to me to be impossible. I'd suggest it being impossible for any of us to prove WHY two different powders (whether they're clean, dirty of whatever) differ in whatever is chosen to matter.
(maybe I will try decaf first)