Wow. Would’ve been good to know when I did this:
One of those instances where larger mud tires and mechanical LSD or lockers will had faired better for you. BLD would have not saved you from that alone as you want momentum and wheel speed to sort through something like that. I don't know the details/conditions of the spot where you got stuck, i'd imagine myself in that situation trying 4hi and lots of gas before entering the mud pit
from the pic it seems the truck is high centered on the diffs so not a lot you can do once you get to that point.
BLD works better in this type of situations where at least 2 out of the 4 wheels have something to grab on, you don't have to wheel the vehicle like you will with an open diff, just keep your foot in the pedal even if the tire is lifted in the air, smooth and steady throttle and the system does the rest.
Notice the first 2 vehicles demonstration with tradional open diff, our trucks are basically open diff front and rear unless you have the factory rear LSD, but we have the same Brake Lock Diff assist found in the Jeep Wranglers since 2007, Notice how the Jeep Wrangler handles the same obstacle. Little wheel spin and up she goes. The 1st video i posted with my RAM above is literally the same condition you see here but with big deeper ruts, the BLD system makes it looks super easy
My Jeep Wrangler Sport below did not have locker or LSD, so she was fully open front/rear diff with the factory BLD system, later on i added an Eaton elocker rear and detroit trutrac front to handle the rocks better.
My FJ for example had A-trac (similar to FCA BLD above but you have to press a switch, i had a rear locker in the FJ though)