To start with, I block all the holes and tennons where the parts come together with white tack before I take the model out to prime. I prime almost everything brown as the base for the wood, and just work at adding bits and colors from there. May seem strange but it works for me. So here was the work I got done last night prior to spraying on the brown. Also note that I've assembled the stone parts and put the front piece on the bottom frame prior to any priming.
So after I got all the prep work done I did a majority of the priming on the sprues so that I could get both sides(aside from what you see in the picture above). Afterward, I clipped everything off and cleaned up some mold lines and did a quick dry fit, and then another quick priming to touch up the areas that were affected either by the clipping or the mold lines. What I had left was pretty much this:
So in order to paint the insides as thoroughly as the outsides without getting frustrated and pulling my beard out, I pull everything apart back to it's original pre-assembly pieces (with a few exceptions, such as I've already glued the stones together, etc.). You can see where I've still got bare plastic at the assembly points so I can use plastic cement for a nice, strong bond.
Something I also like to do is put a long piece of sprue onto the bottom of rats that will need painting. Again not that I've pretty much assembled the plague monks and the plague priest as they will go on the model, but will be painting them off the model for ease.
I also leave the wheels on the sprue until I've painted all the wood and such inside, I find they take a lot less damage in between painting sessions just from being knocked around, and are much less likely to get lost when they are bunched up.
I'll be happy to answer any questions you have about the process. I don't claim to be a pro painter, and I'm not looking for gold daemon level results, I don't have the skill or patience for that, but I do have a knack for getting big stuff (or even little stuff) painted and on the table top in quick order, so I hope to share some of my methods so these large center-piece models don't seem as intimidating the paint.