I don’t do any stirring during my mash – I let it sit, and I often get over 80% efficiency. I also use water to grain ratios that are somewhere around 1.5qt:1lb (when I have room), so I’m not sure you need to factor stirring space in on the equation.

I do find that the thicker my mash is, the harder time I have getting my beer to be clear at the end, but I can’t tell you, on a science level, why that would be.

Finally – my normal solution for making big beers and fitting it into my mash tun is to make smaller batches. I normally make 3 gal. batches of my big stuff vs. 5 gal of “normal gravity” beers. That way I drink them at about the same rate, too.