Residential ranges are insulated so as to not be a fire hazard.
Do you have room to cheat the uppers over? I was working on a large apartment complex and the sub doing the overflow kitchens I couldn't handle installed in the manner you're describing.
I took 1/2 inch out of the filler on the other end and rehung the uppers as 1 piece, only took about 20 minutes to fix.
The uppers can be slightly offset from the lowers without it really jumping out and catching the eye. Happens sometimes on stock kitchen installs when one of the walls is out of plumb 1/8 inch per foot

and you're already maxed out with a three inch filler against a BCC.