The most important thing for getting "accurate" bass, avoiding "boom", or "muddiness", or to get the perception of having "quick/tight" bass will be with where you place yourself in the room, and where you place the subwoofer in the room. In fact, you might consider getting two lesser subs, particularly in your case, to go a long ways in evening out your room modes. The way I typically explain it to friends (don't have scientific evidence, but can link white papers for you) is having one sub is 50% the way there, two subs 95% there, four subs 99% the way there, and "infinite" subs filling the entire room as 100% the way there. This comes from someone only using one sub atm.
Of course acoustic treatments can go a long ways in treating your room modes, and most particularly for bass. Bang for spots are to treat boundary meetings, particularly on the front wall. Still, even the professionals who sell these things would tell you that placement of listener+sub is still the most important. Try to keep yourself off the back wall. Try 38% room length of your ears in the room, if possible, doesn't matter front or back.
Sumthin' to chew on. I hope I beat the horse enough times so that it's soon dead. I'm doing so because many hobbyists are very keen on output and extension, whereas you are not.
Perhaps a couple of Dayton kit subs at your budget, with some added damping materials inside of them. Dunno, good luck!