Hey Bob,
I have almost the exact situation as you. My room is 30ft x 31ft with 9ft ceilings. It is one big room with no partial walls. One side of the room includes the walkout area to the back yard and HT area. The otherside is the pool table and bar area.
Prior to the basement being finished I had all my equipment upstairs in the living room, which was 15 x 18. I had m60's, ep350, vp150, and 4 Qs8's. Things were great.
Then, when I moved everything downstairs, things were still pretty good, however, I later decided to upgrade to the ep500. The cabinet size of the 500 and 350 are similar, however, the more powerful 500 and DSP design outperformed the 350 easily. I now have an ep600, which does a better job than the 500, but they are pretty close.
Axiom now has an EP400, which is an amazing sub in a compact design which has more power than the 350, and is a little cheaper than the 500. In reality, there is not much difference in size between the 350, 400, and 500, so I suppose it is more up to your budget.
Nick is right, that is a big space with a lot of volume. It might be a good idea to consider a little bigger sub if it fits your budget. You could always go with m60's which I owned for over 2 years and they did great in my basement, I now have m80's.
Also, if you order from the factory outlet, you will save 10% on top of the already 5% you get if you order 5 items at the time of order, this may help.
good luck...randy