Considering that you have a good amount of open room volume, I would urge you to up the budget to the 2000 Pro series, and regardless of that: GO PORTED!
Boominess is going to be because of poor placement (like hard up in a corner). Most modern subs of the quality we like to recommend here are not inherently boomy.
Regarding the size of the Sub:
Unlike speakers, the Sub will work on the whole open space, not just your listening "area." I am not suggesting you try to pressurize the whole open space, but all of that space will effect the performance of a smaller Sub like the PB1000.
Also, with the PB or PC 2000Pro, you get more options for tuning the performance of the Sub.