I have never run 5/3/1 but I would think that you can follow something along the lines of this type of periodization. I think it really comes down to the assistance and knowing yourself.
The accumulation block could be say 8 weeks or 2 cycles. Starting with a lower training max (obviously) thus makes it so that weights are lighter and you get more volume in even on the core lifts. Perhaps during this time you wouldn’t absolutely murder yourself on the top set. Then you would do lots of assistance. Do whatever you think is most productive for yourself. BBB, speed work, rep work or whatever! just a lot of volume focused at correcting weaknesses. Again all of this is speculation and you need to decide for yourself as to what is best for you: all out on core lift, extra core lift work, lots of upper back or whatever! just be smart and fix your weaknesses. Do what you hate to do!
Then the intensification block could be 4 or 8 weeks and during this period your training maxes will be higher than the accumulation block thus decrease volume on cores and increasing intensity. During this period volume of asistance would decrease in favour of some movements more related to the core work. This is obisouly up to the lifters discression.
I think this would work quite well. Unfortunately everyone is unique and experience is the only way to figure out what will work best for you!