Honestly, I think I would drop the reroll all together. Make it a 2 die turret range 2-3. Add in a charge based bonus attack for the "twin." Two charges recurring, spend two charges to perform a bonus attack from this turret, allowing the double tap only every other turn. Maybe have it take up a turret slot and a gunner slot to future proof. Range bonuses and overall lack of free mods would hopefully tones this sucker down. Dorsal is rarely taken because of the 2 die attack rarely doing damage, so I don't think it would be OP.
For a Synced Turret, keep the required lock to fire from 1st., but allow a single reroll FCS style. Might be a problem with the VCX or a Lok w/title as those could have the sensor FCS and the Sync reroll. But then again, Matchstick isn't exactly blowing up the meta with his multiple "free" rerolls, so maybe it wouldn't be OP.