Sounds like you are really strapped here.
Definitive Technology has powered subs in some of their speakers that I've heard good things about, but I don't think there are any that are going to do what a good sub will do.
I would not attempt IB until measuring the response at that location, which would require a sub in the listening position, plus REW or some method of measuring. IB might be your only option, but if the response there is problematic... no room gain... tapered low end response, you'll be no better off than with powered subs in your mains.
This may sound a little unusual, but what about smaller sub boxes with good bookshelf/monitors placed on top of the subs?
Also, have you looked at any of the cylinder subs yet? The WAF is sometimes better with those and then sometimes worse...
Can you take a snapshot of your front stage where your speakers are going and post it?