So I think part of the problem then is that I'm not quite wrapping my head around getting the amount or wert you need from a mashing. Say I wanted to do 15 gallons, would I do enough runs to get that much out of the mash or would I do a run and add water to the wert like in previous extract brewing that I've done?
According to
this calculator you'll need about 25 gallons total to get 15 gallons of wort, for a pretty standard grain bill. Your mash will need to be around 13 gallons of that, then you'd sparge with the remaining either all at once or in batches, or fly sparge. You'd be limited by the size of your MLT especially if you want a thinner mash (I shoot for 1.5 qts/pound), so if you really need to get 15 gallons at a time into fermentation, you'll probably need to get a larger picnic cooler, 60 quarts or better. You can certainly use this for smaller batches as well, just be careful to add a degree or two to the strike water to account for the heat lost into the head space and insulation of such a big vessel.
I use the calculator so I know how much water to have heated and waiting for sparging in my HLT. You probably don't want to just run sparge water until you get to your volume, as you will eventually be either extracting tannins (maybe, not much of a danger in batch sparging) or basically just running water through and not extracting anything. You will need to do a few batches to know how much you lose to your equipment and what your efficiency is, there's not really an easy way to calculate what will happen to you in the real world ahead of time, but it definitely helps to be as prepared and planned as possible, IMHO.
Bear in mind you'll need a larger pre-boil volume, ballpark figure is about 10% loss in volume per hour of boiling, plus whatever you lose to trub, hops, etc. You might be looking at up to 18 gallons of wort pre-boil. You can always top off if you're low, or boil longer if you have too much wort.
You could do 10 gallon batches with higher grain bills at a slightly thicker mash in a 10-gallon cooler.
And, of course, you'll need enough fermentation vessels to hold all that beer and account for krauesen/blow-off.