Hm, every barometric stove I've seen so far had the old style box with angle iron corners. Thought maybe they only made them before the body change in 1980. Yours is probably a transition stove right around that time. Old box dimensions built in the new style for 1980. Both were available in 1979 as the change was taking place.
1979 III Manual with both styles available;
Not common with a barometric box, that's for sure.
Here's the back of a Grandma III from Colorado. The tag was attached to the rear shield incorporated into the round corners from 1980 up.
Yours would be a II, the upper brick course was also added in that revision. Not all had them, and they don't show any signs of discoloration or warping without the second course.
The bricks in the old style box you gave dimensions for required cutting. You start with full bricks across back, then start with full bricks down sides installing rear towards the front. You will have a space in the front to fill in with cut bricks, but I'm not sure about your cut sizes. Grandpa takes a 2 9/16 filler piece, but the brick layout pages for Grandma is in the shop. I can look it up tomorrow, but yours may vary since we don't know if your new style box is made to the exact dimensions of the older prints. I can only let you know what brick size was called for with the old box with welded corners. (the model II) Once you know the cut size for the sides, the bottom gets the same size filler piece across front as well. (bottom bricks lay lengthwise across stove - full bricks on left, partial cut brick on right as needed)
You want to vacuum the stove well as you go, or they won't lay flat and fit good. They cut easily scoring with a masonry blade in a circular saw dry. Then snap clean. They are softer than a regular building brick. Don't be too critical of space between them. It will fill in with ash soon enough as you found out removing old bricks.
Be aware your first fire is going to use a lot of BTU steaming off the moisture in the new brick. So the stove won't seem to put out much heat until evaporated entirely.