Cadence CSX-15 MkII was measured here and found quite disappointing with several severe design flaws.
That doesn't mean than CSX-12 is as bad, but draw your own conclusions.
For room your size you are NOT going to find a GOOD sub for your budget. No chance.
The only sub with comes to mind to be able to perform somewhat competent for this puny budget is Premier Acoustic PA150
you could find it here - with some cosmetic wear:
Premier Acoustic PA 150 Subwoofer 15" 1000 Watt Sub Chip and Dent | eBay
benchmark is here:
here is option b)
Dayton Audio C1500K 15" Powered Subwoofer Kit 300-770
I'm not typically a fan of Klipsch subwoofers , but Klipsch RW-12d offers good value for small to medium sized room. (You room is easily in large size category due to it's size and open to other spaces (kitchen) )