Given that you don't want to upgrade your AV Receiver at this time, I'd suggest going with some rather efficient speakers.
Normally, in a large room, I'd be recommending something like the Inifnity Primus or EMP Tek Impression series speakers - particularly when "lower is better" in terms of the budget.
But both the Infinity Primus and EMP Tek speakers love and need some pretty beefy power, which your current AV Receiver isn't really prepared to supply!
So I'd point you more towards
BIC Acoustech and
HSU Research .
This is all about working with what you have, keeping the price down, and keeping in mind your room size.
As others have pointed out, your real challenge is going to be the bass. With big, wide open space, you're going to need a ton of bass output. So your plan of maybe upgrading in pieces at a time is a good one. You'll be able to afford a larger, more powerful subwoofer, or multiple subwoofers if you're able to save up in between.
I agree that the $750 price range is likely where you want to be in terms of getting enough bass output for your room size, but still keeping the price somewhat reasonable.
HSU VTF-3 MK4
Outlaw Audio LFM-1 EX
SVSound
PB12-NSD or
PC12-NSD
Those all fall into that range. And then going a bit more expensive:
Power Sound Audio XV15
or the really big guns:
HSU VTF-15H
If your budget is truly flexible, then sky's the limit! But you're rather limited by your AV Receiver, and you've expressed a desire to keep the price relatively low, so this is the way I would recommend going. Splurge on the subwoofer(s). Go for highly efficient speakers.
Hope that helps!