You give dimensions of 10", 14 1/4" and 32 7/8"; are these from the inside corners or outside?
1 3/4" is nominally a decent minimum top gap dimension for a 5" system, but could the barrel top be warping in? Or is the 1/4" plate the whole top? How concentrated is the heat at the barrel top? A small spot, or the whole top evenly hot? The smaller the gap, the more the heat will concentrate, but if it is too small, the heat may not be able to build up in the first place.
That amount of perlite
should give sufficient insulation where it covers, though the steel will conduct heat away to the feed, cooling the burn tunnel some. Does the insulation extend to the feed end of the burn tunnel and around it? That junction is possibly the hottest spot in the combustion path (someone else who built a steel J-tube has photos of the glowing areas), and leaving it bare might critically reduce combustion effectiveness.
What did you use to contain the perlite?
As your combustion zone is distinctly smaller than your exhaust, it might be that the draft is pulling air through too fast and cooling the fire too much. What kind of chimney do you have on it? What dimensions, and what enclosure?