How do I take down an internal wall tied into a load bearing wall?
I think your plan is correct.

I would speculate that the brick wall was the exterior wall at some point, and that construction is similar to modern veneer brick exteriors, where a freestanding masonry wall is 'tied' into the interior structure, mainly for support (the interior house supports the exterior veneer wall from sway).  Your setup uses bricks for tiebacks; currently, galvanized brick ties are nailed to the structure.  A single wythe of common bricks is rarely structural, being inherently unstable as the wall rises.