On a side note,are you planning on doing a mash out after done mashing? Depending on your mash, if you don't recirculate, which it seems you have a simple mash, some people (me also, but I batch sparge) add enough boiling water to raise the mash temp to around 170F, stopping the enzymes and lowering the viscosity of the wort so that it will flow easier. It may help efficiency with super high gravity wort. You're basically just getting the mash ready to sparge, since you are done converting starches.
I would guess you'd have to stir that, then just let it settle for a few minutes and then sparge?
I never really thought about NOT stirring it, I wouldn't think it would take that long to settle - maybe you're over thinking it?