Need help choosing a second sub

I would try and find another matching Omni S12 if you can. Otherwise I would stick with a ported design that has a similar frequency response. The $500 shipped SVS PB-1000 might be a good match for the S12. When adding multiple subs it is much easier, IMHO, to integrate two matching or at least similar performing subs vs two different performing subs. If you go with two different subs, you are going to need to spend some additional time integrating them. Since your receiver has Audyssey MultiEQ XT it will help with EQ, but you may need something like a MiniDSP to really integrate two different performing subs.

Even with matching subs you really need to measure them to see how they play together. So I would also start researching a tool like REW and pickup a plug and play mic from Minidsp or Parts Express:
http://www.parts-express.com/pe/showdetl.cfm?partnumber=390-808
http://www.minidsp.com/products/acoustic-measurement/umik-1

REW is free, so you are looking at under $100 to have a good measurement program and microphone to help you measure your response and how the subs play in your room with Audyssey XT.

At this price point, my recommendation would be a SVS, SB12-NSD.

I'm not a fan of mixing and matching subs but the above should blend fairly nicely. I'd also give consideration to a SVS, PB12-NSD as the PB1000 is a ten inch driver and wouldn't be able to keep up with the 12" Mirage sub you currently have.

(sorry for my recommendations being above your stated budget)

It depends on the specs and quality of the driver. There are smaller drivers that can put larger drivers to shame in terms of output and extension. SVS uses good stuff. Still, you have a point and the OP should probably call SVS if he decides to go that route to see what they recommend with the Mirage S12. OP, I would see if there are any used S12's floating around near you.

Try to swing for a Hsu VTF2, right now there is a small discount which brings it under 600 shipped. It'll cream the Mirage and SVS subs in output, and have terrific sound quality as well. It is a bit larger and heavier though. For a 6k cubic ft room, more powerful subs are recommended than any of these anyway, but if you think the Mirage is good, you will really like the VTF2.