Off the top of my head for recoil comp:
Heavy Barrel
Folding Stop
Higher Strength
Remember Heavy Weapons is used for firing a grenade launcher (like the one on the Ares Alpha)
You can also pick up the little pistol grenade launchers if you want a more concealable use of the skill.
As for the Alpha:
Accessories: Sling, Shock Pad, Gas Vent 3
Mods: Heavy Barrel, Personalized Grip
Leaves you with RC of 9, 2 slots, and an underbarrel accessory.
The thing is, Heavy Barrel only works with Full bursts, which I'll never have enough RC to do with machine pistols. Likewise, folding stocks, while not "illegal" on a machine pistol, do sound a little silly if you're planning to dual-wield them. But you reminded me of the underbarrel weight, which would be a good solution for the pistols.
LIkewise, I don't think you can use a sling with an Alpha, as slings say that they're only usable with longarms and heavy weapons (the Alpha is an assault rifle, which falls under Automatics). I could put a Lanyard on it, but there's no RC there. Also, according to Arsenal p148, Sling and shock pad aren't cumulative with each other anyway.

Oddly enough, Heavy barrel will stack with anything, so you could combine it with an underbarrel weight. So if we swap out the Sling for an Underbarrel weight we get a full 9 points of RC for a full burst, but it looks like I'd be one short of the necessary slots, according to Chummer.

Btw, I figured all of this out while the forums were down for me....I also found a better way to do the machine pistols by dropping the Crusaders and going for the FN 5-7C (which has RC 1 without gas vents) instead:
FN 5-7C
+ Gas Vent 2
+ Underbarrel Weight
+ Personalized Grip
Total RC of 5, which is enough to support two burst fire shots.