The things I'll do for an externally venting range hood

We knew that there wasn't an existing exhaust vent in our kitchen when we purchased the house.  It seemed a trivial thing to install--run it between the floors in the ceiling out the back or front of the house (giving us some options!).  Unfortunately, the construction of our townhouse is crazy, and there are random perpendicular, load-bearing joists in all directions from our range, so literally no access between the floors for the exhaust.  Our contractor confirmed this when he opened the ceiling, ending the email with "Guess you'll have to get a recirculating hood".  No!  I will NOT have a recirculating hood!  I had a brilliant (foolish?) idea while in the shower to build a soffit to house the ductwork, but since we already had our cabinets, the ductwork has to make a convoluted path from the hood, up into the ceiling in the kitchen, dropping down into the soffit in the dining room to finally exit the back of our townhouse.

Here's the framework of the soffit in the dining room:

It's going to have two recessed directional lights to shine some light on the beautiful paintings made for us by my father-in-law.  We also need a tiny soffit above the hood in the kitchen as well, again, because of some wacky placement of joists in the ceiling:

I have a hood!  There is light at the end of this...ductwork (or something :).

Good plans in theory and underway, but....we've been stalled the past two days with having to get approval from the HOA (since the vent affects the exterior of the building) and our neighbor (potential noise) before we could get a building permit.  And we may still have problems since the vent is less than the required feet from an open window.  But, we have a plan there, too....