I was contemplating a similar thing, but only had two bays spare.
Luckilly the fan controller gubbins arent too deep in the void, so i cobbled this together

- Hopefully some of the pics may give you some ideas.
The bays are perfectly positioned for air intake across the CPU coller and cross flow to the rear exhaust fan.
View into the bays
As i have tree bays in use a 120mm fan wouldnt fit and with the hot days weve being having i wanted a bit of extra air flow throughthe case and cobbled this togethre as a temporary solution with a spare fan i had knocking about, but TBH it works that well im probably gonna leave it in place
I rook the fan, and using the standard screws attached some 90 degree metal angles i had in the garage (B&Q 4 for £2.50 or something like that) to the four scew holes:
Two angles on
And another two
I took out the fan controller and then screwed the two bottom angle pieces to the runners.
Attached on the Fan Controller runners
This site the bottom of the fan level with the bottom of the controller, enabling you to fit the fan in the three bays, but using the space behind the fan controller
As you can see, fits nicely into the space available
Going In
You have several options on moving the fan further forwards / backwards on the rails to position it wherever is most suitable for your setup.
I put mine towrds the back (deeper into the case) and was able to angle it slightly downwards (which after some trial and error gave the best cooling).
Inside the case
I then had the dilema of what to do with the open void with thoughts of meash (to match the side) but didnt want to just leave it open (even though the door is almost always closed).
Just to see what effect it had, I just clipped the blanking plates back into place and to my surprise, due to the fit (or lack of) the blanks there was no affect on the temps, so ive left them in.
Linky