Transmission line idea, will it work?

The important part of the design are the top two diagrams, the third can be changed. Will a 4sided transmission line work? Dotted lines represent a square brace going all around to connect the two boxes. Each brace will be hollow to allow air to move out.
63E3DD26-8797-4299-8EE6-4023729CBA59.jpeg
 
By 4-sided you mean 4 terminus? As drawn it is only one, and as an aside the line is not long enuff to be practical. And given the shape we have an expanding line which needs to be even longer. It also usually needs a driver offset which is not possible with this topology (if you want less ripple).

I have started a sketch of something simialr (but a dozen sides) for a midTL.

dave
 
As I understand your drawing you're making what I refer to as a big vent reflex (BVR) in that the TLs vent 'dumps' into a large perimeter box vent, which is the theoretical ideal since the driver is in the vent per the original BR patent and Olson's successful BLH (unfortunately don't remember the model # and my info is on a damaged HD :cuss: :headbash: ).

In short, I say go for it if HR or similar can sim it close enough! 👍😎

The more I look at it though, it's not the same, but interesting enough to try a POC anyway.