Sounds like you've got a huge space to fill with bass. I'm not sure you'd be satisfied with a single sealed driver considering it sounds pretty large. Your best be would probably be to have chalugadp cut you a custom flat pack with a ported design. If you were to build the enclosure to your max dimensions you'd probably land somewhere in the 9 cubic foot range for internal volume. If you went with a SI 18 you could tune it pretty damn low so for HT you'd be in good shape. I know a lot of guys run SI 18's in about 5 cubic feet... if it's possible to get away with them in 4.5 cubic feet you could even run two dual opposed in that maximum sized enclosure and would just end up with a higher tune but twice the cone area which may be an option. I'm sure a few others with more experience can chime in on whether or not that's a good idea.
Two of those drivers I believe costs around $350, the Nuke3k dsp $280, which leaves you $370 for the box which I believe would take 2 sheets of MDF and I'm not sure what chalugadp would charge for it. Something to think about though.