Things you might consider.
If you build a sealed sub, the box build is simpler, but everything else is more complicated. In a sealed design you need a much more expensive driver, with more amp power and need Eq and a high pass filter.
If you choose the right driver and design the cabinet properly you just need a good driver a well designed and built cabinet and a modest amp.
For instance I bet if I modeled
this driver it would make a nice ported or ABR sub. The unit is efficient and has pretty much all the T/S parameters in the sweet spot. It is a little short on xmax, but with the sensitivity of this unit it won't matter and I believe would power your space nicely. If you are interested in it, I will model it for you.
I think you would come out well within budget and keep your "Trouble and Strife" happy.