If its really a mixed bag of texturing jobs and allot of sanding is in store, you might have two options:
1) sand, sand, and sand. The dust if not tented off will be with you forever.
2) re float the entire wall area after doins some sanding to smooth of the thick areas and start from there.
3) forget number one and two and hang new 1/4 inch rock on the walls and go from there.
This is a tough call as some areas could be so splotchy and thick that sanding and re floating is very impractical. I would suggest in using the paint striping tool that you draw down like a draw knife. It will knock off the areas rather quick and effecient. This tool comes in size heads up to 2 1/2 inches. Works good on paint chipping and this is not that different.
Re floating is good when the area to be smoothed out is not too thick. I mean maybe 1/16 of an inch or a tad more.
Re hanging rock is so fast and you start off with new walls, but you do have to remove all the molding and simply re install after the rock is up. cutting out of electrics is a small process and obtaining longer screws for the plates.