It's understandable how "X Shot Bonus Potency:" is confusing. It means, "This is the total potency of the attack when the previous shot triggered its proc"; not "This is bonus potency in addition to the base potency when the previous shot triggered its proc". Compare to ammo: "Ammunition effect: Increases current X Shot potency by 30"
Ammo no-proc Slug Shot (130 potency) + proc Clean Shot (240 potency) = 370 potency / 2 GCDs = 185 potency / GCD
no-ammo Split Shot (160) + ammo+proc Slug Shot (230) + proc Clean Shot (240) = 210/GCD
2x no-ammo Split Shot (160) + ammo+proc Slug Shot (230) + proc Clean Shot (240) = 197.5/GCD
3x no-ammo Split Shot (160) + ammo+proc Slug Shot (230) + proc Clean Shot (240) = 190
4x no-ammo Split Shot (160) + ammo+proc Slug Shot (230) + proc Clean Shot (240) = 185
So you can fail to get a proc on three Split Shots in a row and it would still be the same damage/GCD as skipping Split Shot and using QuickReload on Slug Shot. The probability of failing four procs in a row is 6.25%, so you have a 93.75% chance of doing at least that much. The probability of failing three procs in a row is 12.5%, so you have an 87.5% chance of doing better by starting with Split Shots. It's a little bit more complicated than that because you don't want to be sitting on Quick Reload forever, but that's the basic idea.
Have you considered doing 1-2-1-3-2 instead of 1-2-3? Ammo will give +30 potency to any shot, so let's ignore that part of the ammo effect for a moment--it doesn't matter which shots that gets applied to. The difference in which shots you use ammo on will be the forced procs in your 1-2-3. Since each shot already has a 50% chance to proc the bonus for the next shot, and a 50% chance that you'll have to go back to Split Shot, we'll attribute half the difference between Split Shot and the powered up Slug/Clean shots to ammo's effect. That means ammo is worth an additional 20 potency if you use it on Split Shot ((200-160)*0.5) or an additional 40 potency on Slug Shot ((240-160)*0.5), in addition to the +30 potency that any shot gets from ammo. So if QuickReload is almost ready, you can tweak your 123 to fish for an Enhanced Slug Shot to use with it.