as others have mentioned, I would definitely use kettle and not fermentor as the target. the quantity of beer left behind in your kettle does not change anything in terms of the beer itself (only the amount). Brewhouse efficiency is annoying in my opinion and confuses things. Mash efficiency is a far more useful metric. I don't use brewer's friend but I punched in your fermentables and volumes and get pretty much the OG you measured at a 70% mash efficiency.@jdudek I do not have an official pre-boil volume, just one that I can estimate. I began the BIAB with 3.50 gallons, poured over with another 0.25 gallons for a total water amount of 3.75. I tried to squeeze the bag to extract as much water as possible. Based on other's who have done the measurement (something I will try to do moving forward) I can assume I lost 0.07-0.08 gal/lb to grain absorption, which would bring my preboil volume down between 3.31-3.36 gallons.
In others' experiences, is brewer's friend usually pretty good about predicting OG? I know I was entering 3.75 gallons into the pre-boil volume instead of the corrected amount, but even when I switch that to 3.33 it does not change the predicted OG (at 68% brewhouse efficiency) and I entered 3.33 preboil, 2.75 post boil, with 2.25 hoping to get into the fermentor and the OG remains 1.063. Interestingly enough, when I change the target to boil kettle and enter 2.75, my OG drops to the 1.051 mark which is much closer to my measured OG.
I have no idea why entering the post-boil volume of 2.75 gallons, leaving 0.5 behind and getting 2.25 gallons to fermentor changes the OG. Any guesses on this? Am I over manipulating the software at this point or just using it wrong? The OG in the trub should be the same as the OG in the fermentor. Should I just use it like this?
I'll try a dunk sparge with the next brew as well now that I have access to my bigger pot again.

It's wonky that pre-boil volume does not make a difference in OG, but that's probably because BF has you entering your mash efficiency which essentially already accounts for all these numbers. What should really happen is that efficiency should change based on the amount of pre boil volume. More volume (better squeeze, or sparge), more efficient. Since the efficiency is entered as a hard number, then you can enter any odd number for pre boil volume and BF is happy. It's what most brewing software does, not optimal in my opinion. A predictive model is a lot less frustrating