If you are concerned about damaging insulation during transport, I would advise making a sheetmetal wrapper with an inch or so of space around the burn tunnel and riser, and filling that with insulation. Coarse perlite mixed with a tiny bit of powdered clay and moistened would hold its shape and not spill out of gaps. Maybe you could pour perlite into the gap, then drench it with muddy clayey
water and let that dry out with some heat... I haven't tried this so don't know how well it would work. If you add standoffs to keep the wrapper evenly spaced from the core, fiberglass or rockwool would work fine.
Note: an easy way to make a wrapper would be to put some 6" galvanized duct around the 4" steel core. This would give the most insulation at the flat sides which will get hottest, and be safe and easy to move around.