I am a big believer in BBB as a provider of the volume of training that my body needs. I have used it in some form for the last couple of years, and never get very far away from it. I would consider simply starting the challenge over with your new training maxes. I promise, it won't feel the same as your first time through the challenge. You'll learn new things about yourself.
That being said, I compete as a power-lifter, and after running the challenges "as-is" a few times (this is important, as if you never run the programs as written, you don't really know if they work for you), I'm learning how to tweak things even more to my advantage.
Over the past 4 years or so, I've started to realize which version of 5/3/1 works best for each of my big 3 lifts and will be testing my current theories at my next meet in April:
Squat: Good ol' 5/3/1 going for extra reps and/or jokers (depending on how close I am to a meet). I also utilize a second squat day late in the week with a safety squat bar in which I am on the BBB 3-month challenge (this will end a week earlier than my other cycles to allow for accumulating some strength). Something about the lighter weights and high volume really helps my squat.
Bench: I simply do the original 5/3/1 and some heavy singles thrown in occasionally- my shoulder can't handle a ton of barbell pressing, so I do a lot of bodybuilding-type stuff twice a week to put on the muscle I need. This has worked well my last 2 meets, so have stuck with it. If I do any BBB 5x10 work, it's with a football/swiss bar using the inside grips.
Deadlift: The 13-week challenge was money for my deadlift (went from 385 to 410 in just those 13 weeks). I adjusted the percentages (lowered them 5-10%) to allow me to pull from a box, and the 5x5 through 5x1 weeks made a big difference in my speed off of the floor in normal depth efforts. The soreness every other week from the assistance weight moving up was pretty debilitating, but well worth it.