My $0.02 is that stirring during the mash shouldn't matter. I don't do it (granted I use a mash tun, but still), never did, and I get 80% every time. I stir like mad during dough-in and while I'm letting the temp drop to where I want to mash (I dough-in on the high side every time. Easier to stir-down a temp than frantically try to add more hot water). I use a wire whisk and have zero dough-balls (this is crucial) when the mash starts. I also whisk it before running off (or pulling the bag, in your case). I then whisk again after the sparge addition (or when you've lowered bag into your sparge pot, in your case). Other than that, during the mash, from 60-480 minutes (yes, not a typo), I don't stir once.
If you're sparging, I'd consider doing a larger sparge. You might get a thinner grist, separate some grains that were stuck together before, release more sugars clinging to particles, etc. The crush looks good, but I bet you can go just a smidge tighter, too. Mine is finer than that and I use a mash tun.
Stir the bejeebus out of it when you dough-in (dough-in high so you have time to stir), before you pull the bag, and while you "sparge". Holding the mash temp shouldn't affect your efficiency one bit. It affects attenuation, but that's another topic.
Don't rush anything. That's why I dough-in a tad high. Give myself plenty of time to stir. You won't denature beta-amylase in the 5 minutes it takes to come down from 160 to 155, trust me, I do it all the time. Don't rush the process after the mash either. There is no need to get anything done by a certain period of time. 5 minutes longer here or there won't affect your beer much at all (until we start talking hops, later, but this is regarding mash/lauter).