If you want the J-tube feed to stick out of the front of the wood box, an 8" core can work fine. Given the framing between the brick box and the doorframe I would go with 3" of cob over the brick - enough to be sturdy but not take too much space or too long for heat to start to come through it. My recommendation would be an 8x8 feed opening, 8" x 9" high burn tunnel with 8-10" long roof, and 8" diameter riser from perlite-clay. You can line the floor with an inch of strong cob, or pieces of firebrick split 1 1/4" thick, to get the right dimension without cutting lots of firebrick. From my experience, you want about 2" thickness on the riser which gives 12" outside diameter. The simplest way to make this is with a piece of 8" sonotube and a pair of 6" stovepipe sections bent out and snapped together to make a 12" sleeve. As it commonly comes in 2' lengths, I would advise three pieces of stovepipe with one cut in half and fitted to itself, giving a 36" height to set on top of the burn tunnel walls. 36 + 8 = 44", which is just enough for an 8" J-tube with 16" high feed tube. See
my RMH build for riser construction details.
You need some insulation under the core so the floor doesn't suck heat out of it; an inch or two of perlite-clay under the core would do the job nicely, with scraps of 1 1/4" firebrick at intervals to stabilize things. To strengthen the core, especially the feed tube, I would surround it with at least 4", 6" would be better, of cob with some perlite mixed into the inner couple of inches. This would give a pretty good mix of strength and insulation. I would use a good amount of straw in the main/outer layer, around the feed and around the brick box, so you don't get large cracks.
For the bell bench, I would make walls of 2" thick block as you mentioned, and internal piers of 4" hollow block on end to support the roof, spaced as widely as you can while supporting all the roof panels. I have found 16 x 16 or 18 x 18 concrete pavers at Lowe's or Home Depot, and those supported all around the edges and at corners in the middle will make a good base for a cob seat. The bell cavity will have the coolest air at floor level, but I would still put in an inch of perlite-clay with a smooth hard top for cleanability, after placing structural block.