With an AE3000 at 9 feet from the screen (and that's lens to screen, so if your room is exactly 9 feet long, then you need to deduce another foot or so for the depth of the PJ), the most you would get is 91" diagonal. I used the projector central screen calculator, but I've found it pretty accurate in practice with my AE3000. The Sony comes up as 89" diagonal from the same 9' throw.
I'd recommend you take the screen back and buy one once you've chosen your projector, then you can try the PJ in place to confirm how big it will go. There isn't a PJ available that will be able to zoom big enough to fill it from 9 feet, so it would be a waste, unless you can mask the sides and top to make it appear smaller perhaps? BTW, it's not usually recommended to use a PJ at the extremes of the zoom range, but if you want the biggest picture, I don't see how you have any choice.
Link to the projector screen calculator with the AE3000 already chosen:
Projection Calculator - Throw Distance and Screen Size
Sorry for the bad news.