I need some help figuring out how best to tackle this.

We've got an old attached garage that someone at some point egressed into and put in a large bathroom and closet. We're in the middle of taking that all out, installing a new raised floor and finishing it off entirely as a bedroom.

Now, for the walls, to level things for drywall I will be using 2x2's secured horizontally along the studs @ 16"OC. On top of that will be insulation web, which dense pack cellulose will be blown into.

My PROBLEM is that the exterior sheathing is 1" thick board, which had anything from a 1/4" space to a 3/4" space between them due to shrinkage.

I do NOT want to blow cellulose and have it compress the tar paper against the brick, or fill the brick weeping cavity at all, so I need some way of sealing all these slits.

What do you think the best method would be, beyond having someone come in and spray a thin seal coat of foam.

I could get 4" wide insulation fabric and staple it along the joints. Be tedious considering it'd add up to 1200 feet I'd have to staple over each. Ugh. I could staple in more non-woven fabric, but that'd end up doubling the cost on it, which may not be viable.

Thoughts?