This is a bit over your budget, but my suggestion is to get two Parts Express 10" subwoofer cabinets with cut-outs; two 240-watt amps without bass boost; and two 10" Dayton Reference subwoofers. The Daytons subs come in two varieties, the HF version and the HO version, so you'll have to choose between them. Either one will have more than enough excursion to handle the full output of the 240 watt amp so there's no need to get a longer-excursion woofer like the Titanic. The HF has a bit warmer bass and the HO a bit tighter bass, but they're both very good.
The reasons for using two smaller subs instead of one big sub have been presented in other threads.
Duke
dealer/manufacturer
The reasons for using two smaller subs instead of one big sub have been presented in other threads.
Duke
dealer/manufacturer