Personally when I dunk sparge I mash with the final volume then use the extra water needed for dunk sparging. No logical reason other then that's how I do it.
Do you know what your boil-off rate is by any chance? I ran your numbers through this BIAB calc
and came up with 3.51 gal if you have a 1 gal per hour boiloff rate. But I know that program gives a little extra in my experience. Brewtarget has told me not enough water a couple of times and been right on a couple of times. Personally I probably would go with 3 gal of total water .2 gal extra won't hurt a thing.