Hi Daniel, welcome to Permies. Sorry none of us with information seem to have noticed your post when you made it... I hope you were able to get your heater running well.
Do you still have just a test build outside? (If you have smoke coming out from the bottom of the barrel I would hope it is outside

) I presume you are working on a nominal 8"
RMH. If you built the
feed and burn tunnel 6 1/2" wide by 9" high, that should work fine. You can let an inch or two of
ash stay on the burn tunnel floor without problems and maybe improve the function. The heat riser is better square or best round, but if it burns clean you are probably okay. You can make the riser perfectly 7 1/2" or so square by setting the bricks in each
course pinwheel fashion, alternating direction so each course anchors the ones above and below. The small step in the sides going from burn tunnel width to riser width will not hurt.
The insulating jacket expanding so close to the barrel sides is likely to be a problem once you try to install the core in a complete system. You want a couple of inches clear all around if you can get it. I would remove the lath and perlite, and turn the lath around so the straighter lines run horizontal instead of vertical. That along with more frequent wire ties should keep it from expanding so much when you fill it with perlite.
What kind of mortar were you making? Clay and sand? You need to use very fine uniform sand for this mortar, and mix it very thin and wet so it can make a thin layer when applied. The bricks need to be wetted before setting, too, or they will suck the
water out of the mortar too fast and make it impossible to adjust. Clay-sand mortar is just to fill all the gaps, not to glue the bricks together. The good part of this is that it is easy to disassemble and clean the bricks and
reuse them.
If you have any other questions, please ask, and we will
answer faster.