I'm curious where the exhaust pipe draws from. If it opens to the near side of the core, gases from the bench area would have to (at least mostly) rise back up over the core to get to the exit, making flow to the bench anemic. If the exhaust goes under the core, then hot gases will hardly get to the near side, reducing the effective ISA as if that section of wall was floor.
Having a good gap around the back or under the core would allow the whole bell to act as a single unit. I think 2" would be the minimum, and 3" would be better.
Looking closer at the pictures, I see the pipe ending just at the wall, which would really reduce the effectiveness of the bench, and the core actually touching the brick bell wall. I think, given the footprint already established, your best move would be to elevate the core a couple of bricks higher and leave a large space for cool gases to travel under it freely.