How to join hardwood rows from two rooms at doorway?
I think your plan is good.  I use a metal L to do my transitions like this.  You have to figure out where you want your "perpendicular threshold" boards to start and screw in the Ls on each side.  This way you can start at the doorway and jam the boards against the L.  This will give you a nice straight line.  I have also left the Ls in some transitions and it gives a really cool look.  But if you don't want them then take it out after your surrounding rooms are done and nail in your threshold area last.