Vent Hoods Here! Gots A Problem....

Ha, when don't we.....
The new super fancy vent hood and external blower came yesterday.

Check out what $3k of venting looks like...at least we got free delivery from Atherton Appliance.
Sideview

Dang its big..and heavy...wow...big. This is the smallest hood Wolf recommends for the stove too...
Bottom View

The big holes at the back are for heat lamps..I didn't want em but they come with this size automatically. From what I can tell it looks like a high quality unit.

The Wall Cap

Holy Freaking Moly this thing is huge!!! Like ten times the size of a normal wall vent...so big in fact..I'm not sure that we can use it...This is, of course, a major screw up on my part. Somehow through out this entire process I never happened to clue in on the dimensions of this thing..and nobody else bothered to mention it either...

The Situation On The Outside Of The House

Here's the existing wall vent for the stove.

I'm not even sure that's a legal install. I'm pretty sure you can't vent kitchen oders over an operable window....

Wall Area

This is all the space we have easy access to for the vent duct on the side of the house, between the two soil stacks and above the window,...doesn't look very promising does it...hurray...

But there might be a little bit of hope.
Mystery Window

This is the 'window to no where' that's actually inside the dropped ceiling in the TV room.
It looks to be almost exactly the same size as the vent...
How horrible would it look if we removed the window and put the wall vent in its place?
I'll have to check clearances but I think it will work if we make that window next to it inoperable.

Other option is to return the external blower (probably with a hefty restocking fee) and get an in-line blower and use a normal sized wall vent.

What to do, what to do. Anybody have any useful suggestions?

We Need Range Hood Help!

Arrrrrgh.....anybody ever look at what high end range hoods cost!?!?!
Holy freaking mackerel they are expensive...
What I love is, often you have to buy all the parts separately..so that $1600 for the hood is just for the shell of the hood...its another $1000 if you want a quiet motor option.

Because we have no common sense we want to install the 36" wide pro style stove that we've owned since 2000 in our new super tiny kitchen..don't bother trying to knock some sense into us we're doing it.

Our stove is Wolf model# R364C which you can see below acting as the worlds most expensive cookie sheet storage rack.

We are going to shoehorn it into this space currently occupied by a 30" wide stove.

The Specs
According to the manf I need a 27" deep range hood that's rated at 900cfm.
I can only use a 36" wide hood because of space issues.
I would like it to be as quiet as possible also.
The research I've done so far is pointing me to a remote mounted fan-the type that's mounted externally to the house and has the motor in the wall cap.

Because of the length of the exhaust and one elbow I will need a fan rated at more than 900cfm, 1100cfm seems to be correct.

I've been doing web searches for a while now but I'm not really finding any good hard info to help me with this. Most of the manf sites point you to a brick and mortar authorized dealer and they don't exactly tell you what its going to cost.
I also can't seem to find sone ratings for the different hoods?

Or, the range hoods you can buy online seem to be off brand (at least to me) and I have no idea if they are any good.

Can anybody help me out?
Thanks,