I find it interesting that if we assume that:
1) That two potatos in 1.5" barrels vary in mass by an average of 18% (seems reasonable, given the latke data)
2) That the projectiles start moving at the same time
3) That the speed of sound in the propellent gasses is 3000 fps (it's probably slower by the time the projectile is at the end of the barrel), that your barrels are 4 feet long, and that your (slower) projectile is going 400 fps
Then the first projectile to leave would exit some 10% sooner (on average) - or roughly 1 millisecond.
And that the "rarefaction 'wave'" (the pressure drop) would travel the 8 feet to the rear of the other projectile in about 2.6 ms (because it'd propogate at the speed of sound) - and before it arrives, the pressure at the rear of the projectile is exactly the same as if the other projectile was still in the barrel.
You might think of it as something along the lines of "the other gasses havn't heard the news yet, so they keep doing their thing".
Nothing really new - it's what limits the velocity of sound.
My suspicion is that, because 1 ms < 2.6 ms, the fact that one potato leaves the barrel first doesn't matter.
...given that the projectiles start moving at (or nearly at) the same time.
I'd install a burstdisk to increase the chance that they do.