To better reply to your speciifics:
Seems nobody really adressed what you asked.
I've seen no real difference between IMP & MOD chokes with the use of the Brenneke style slugs. Accuracy depends mostly on what type sighting sytem you have. I've an iron-sight IMP cylinder tube that shoots very well to 50+ yards. My double bead 21" Turkey (vent ribbed tube Mod) shoot them slightly not as well, but certainly good enough to 50 yards.
Longer barrels = better all told, but iron sights, or double beads, can make a big difference. All told, shotguns are a "point 'n slap" interface. Sights likely aren't all that conducive to extreme accuracy (maybe my own take on the nature of the beast).
But, with iron sights, I was doing ~2" groups at 50 yards & with that double bead = call it 3" 3-shot groups at 50 yds. Even 4" groups at 50 is pretty darned good for the power.
Choke really matters depending on what you're shooting.
I've seen not much difference between modified versus improved cylinder for most slugs - depends again mostly on the sights used.
C'mon back with stuff not answered.