I had the original 10" SVS PB-10 in a 20x20 high vaulted ceiling room that was open to the kitchen and a hallway. It did surprisingly well in there, but lacked enough solid output for my taste - super clean and had output to 16Hz, but I ended up upgrading for more output. I sold it to a guy who had a room that was effectively a 20' cube and it didn't do well in there, though I am not sure a single sub is really going to work in a room like that regardless. So taking that into consideration, I think the 10" driver might not be the best choice.
I am also of the mindset that I'd rather buy at the top end of what I want to spend and not have to replace it as well as the fact that this typically also nets you a better resale value (not always, but you get what I am saying), but my budget would also take that into account
As was mentioned, you are not going to get something that will give you reference levels in that room on that budget. The Cadence will do the trick and definitely will be better than the HTIB sub for sure. Note too that it was $399 when it came out.