The main reason I heat mine up is that I can direct fire my mash tun, and I have some dead space under my mash screen, so I don't have to worry about scorching grain. So, toward the end of the mash I turn on the flame and recirculate (by hand with a small pot) the wort from the bottom to the top of the grain bed. This serves a few purposes:
1.) It clears the wort of husk material
2.) It warms up the wort so it comes to a boil more quickly in the kettle
3.) It seems to thin out the wort and it flows a bit better at 160's than it does as it falls into 140's.
I also stir the top 1/2 of the grain bed while I am sparging. Basically, I do some sort of hybrid batch/fly sparge. I am fly sparging as fast as I can get water onto the grain bed, and draining at the same speed. I stir the top part of the grain to keep it from compacting and also to keep the sugar mixed in with the sparge water ...... keeping pH more stable. But, the whole "sparge" process I use is pretty quick. 60 minute mash. 5 minutes of recirculating and heating. (I shut the mash tun burner off when my mash hits low 160's). Fly/batch sparge to collect 8 gallons of wort ...... this takes about 10-12 minutes I would say.
A lot of brewing is sort of playing around and adjusting to your own system. I would definitely start by trying for a finer crush and see where that gets you (it is the simplest thing to try). You will likely need to balance a finer crush with the ability of your system to not have a stuck sparge. Trial and Error..... repeat.