Mark,
As always well thought out trial and error regarding the tunnel placement, and what the look will be leading up to it. As with most projects there can be a ripple effect (pun intended) to the surrounding area as far as looks, access, etc. I think you’ve come up with a solid plan.
As far as the mortar joints, I’ve always used joint compound with pretty good results. I think one thing that might help would be to let the joint compound dry and form a haze, sometimes overnight. And depending on how it comes off of the surface, I will use my thumb to clear off the bricks. If I find that the mortar is staying in the joints for the most part, I clean off the bricks with a lint free rag and a very light touch. On occasion I do need to reapply joint compound to a very small area here and there. I think your use of chalk was inspiring, another tool in the arsenal!
As always I’m enjoying your progress, well done, and I look forward to more.
Andy