Okay, looking over it, here's my suggestion regarding your idea:

Once, Gotei 6 was Gotei 7, having two Divisions focused on battle: Vanguard and Reservoir Division (I can't really decide which is which from the descriptions). The names for the Divisions can really be whatever, the point is that they'd replace any notions of 6th and 11th, because I hate them numbers in this iteration, Gotei may have never had 13 Divisions.

However, for logical reasons, these two Divisions suffered the most casualties and their numbers couldn't justify two separate Divisions, so they were mashed into one. So, their backstory becomes: "Created in last restructuring of Gotei due to losses suffered early in the war, the Joint Gotei Combat Division (AKA the Assault Division), was forged from the deep and long running bonds of the Vanguard and Reservoir Divisions of days past along with a good portion of the Assassins from the now defunct Onmitsukido, and a good portion of the Hado specialist from old Kido Corps who preferred field action to research duty in the R&D Division."

Note: I keep referring to Onmitsukido as defunct because in canon, it'd become joined at the hip with Gotei; logical next step from that would be the Onmitsukido officially ceasing to exist as it is wholly integrated as part of Gotei.