Normaly you do not need multiple turns to assault a settlement if you bring up enough soldiers, and a capable general with you. It seems very unlikely that you would get attacked multiple times if you assault on the next turn you have besieged the settlement. If a garrison is not that big, you might need only 2 rams ( no stone wall, of course, you´d get slaughtered at the gates ), to breach the walls, - one for a gate, and one for the wall not far from it, so you can flank the enemies. Good missile troops support to barrage them from a distance, reducing their numbers significantly, should help as well.
First, i too was thinking of realistic movement mod, but Rebel armies "spawning" near a settlement, epsecially one after another in a single turn is something i´ve not observed yet.
Spoiler Alert, click show to read: 
Btw: just curious if there are methods to prevent Rebell garrisons from moving out of settlements while using realisic movement? The "immovable" trait of the Rebell generals seem not to work any more due to highly increased movement points.
Thanks in adavance, and sorry for OT.