I would first buy a 22 Remington cement nailer. Cheap and does a good job. Nail in some furing strips 16 OC and wide enough for your electrics.
then, cut in the rigid styrofoam insulation between the furing strips. This will save your space instead of your comment about rigid then furing strips.
Now, again to save money and space, I would consider using 1/4 inch drywall on the walls. yes, its much thinner and has that bounce, but, the rock will be right next to the rigid insulation. So, you have the support. 16 OC should take care of allot of that also.
Then do your tape and bed work and then apply the beading or corner molding all around the room.
Now, if it was mine, I would do this first. Use a Ugl brand cement or cinder block sealer for the walls. This is just insurance and precautions.
Then do your build up.
Applying stucco to the basement walls will be pretty rough and cause a big rasberry when you scrape your arm against it.
I would not recommend this.
Will discuss at more lengths with your additional input and thinking.