Ok, so my interpretation of mashout is really about heating the mash into the mid to upper 160F area before first runnings whether you're direct firing, decocting, or infusing. Those of us with cooler MLTs, infusion is the only way. Using beertoolspro, I can tell it I want to infuse into an existing mash with a fixed temp and volume. It will tell me what the new temp will be. Since I can also input and lock in my desired preboil volume, it will subtract the mash out infusion from the 2-batch sparge volumes. By the way, you can go a little thicker on your mash to make room for at least some of the mash out infusion (maybe 1.1 qt/lb).
Here's a rundown of last night's volumes:
Mash 21lbs with 6.5g (1.24qt/lb).
First runnings were 3.5 gallons at 1.075.
Batch 1, 5 gallons @ 178, settled to 166. Running 5.25 @ 1.042.
Batch 2, 4gal @160. Runnings 4.25gal @ 1.022.
Preboil total was 13 gallons @ 1.050 for 87.5% effeciency.
Now, let's say I did have room for a one gallon mashout infusion. I'd just reduce the two batches by 1/2 gallon each.
I think even a one gallon infusion of boiling water will increase efficiency because you're making that sugar more soluable from the start. However, the alternative and next best thing is getting the grain bed up in temp as soon as you can (if not mashout before first runnings, then at least in the first batch infusion).