Either way, although if 1/3 of the water puts you in a good mash ratio then you’ll get better extraction from having two larger sparges.
Having said that, I generally use as much water as possible for my mash, and only sparge with what won’t fit. With my MLT I can do up to 3.5qt/lb so I’ll only have a gallon left for sparge. Its more like no-sparge this way, but I still get my usual 75% efficiency.
I usually figure 1.25 to 1.5 qts per lb for mash, & then split the volume that I need to cover:
Boil-off + trub losses + grain absorption + dead space.
pH is critical to mashing and overall beer flavor. Tannin extraction occurs at a pH > 6.0. It’s usually not a problem when batch sparging, but again it depends on your water profile and you grist.
It’s the reason I went away from the 5 gallon round and use the bigger rectangle cooler or 10 gallon round or my keg with false bottom. I rarely run into the issue anymore and plan my bigger beers for the bigger units. But I add as I go up to half total volume and then same with the second half when absolutely necessary. You guys that go big all the time have these problems more frequently than me with my little brews…