In my experience, crush is always the first thing to look at.
+1 on crush being the first variable to consider and its probably one of the most influential on efficiency. I have to say that the second most important variable is the runoff rate. The slower you go, the higher the efficiency. Even with batch sparging, I'd have to say that extending the duration should have a positive effect. A mashout temperature step to the high 160's is also worth a couple of points increase.
Even though I'm a proponent of getting your water chemistry right for mashing, I'm not really sure that it is a big factor in improving efficiency. A number of brewers have told me that it made a difference for them, but I don't understand why that would be. The only thing I can imagine is that their mashing chemistry conditions were so far off that it was negatively effecting their efficiency.
With that said, I used to get around 80 to 82 percent efficiency with my old system. Then I upgraded my system and my efficiency dropped well into the 70's while I learned what my water volumes needed to be. My LHBS also was having mill troubles and I knew they had poor crush. That moved me to buy a good mill. I now pre-condition the malt before the crush and have been able to crush fairly fine. Since I've figured out the water volume issue and been using a good crush, my efficiency is nearly 90 percent. That is not a good thing when you have figured your recipe based on 82% !!