The only subs that ever made my 3500 cubic foot room feel like my car audio days are not the subs in the $1000 or less category. Including a pair of VTF-15H's I've played with in my room.
You need something in the caliber of JTR Speaker equipment to get there unless you are willing to use many multiple units of the cheaper subs. Your room is MUCH bigger than mine considering all the open airspace. It seems you are only considering small sealed subs and have an exceptionally limited placement option. (who knows how your seating area will sound with your sub in that single untested shelf position)
It effectively amounts to this. If you'd like to experience car audio levels of bass on occassion, but are restricted by the stated limitations of subwoofer cabinet size, subwoofer location, budget, and your fairly enormous room size - you have impossible goals.
What car audio setup did you have?
I had a bunch of different stuff throughout the years, my favorite (even over a many other 8, 10, 12, and 15" name brand drivers) was a single Infinity Kappa Perfect 10.1 in a Infinity made and matching bandpass box in my Acura Integra hatchback. It was clean and pounded HARD for music! For whatever reason that box and my car was an excellent combination. I had a LOT of compliments on that particular setup and know I helped Harmon Kardon sell several additional Infinity Kappa perfect drivers after people auditioned my setup. My JTR Captivator Pro pair gets me to the same levels of bass that any car setup I ever owned was capable of. These subs are not anywhere near your budget, and nowhere near match your size constraints, but something along those lines, be it Seaton Sound, Elemental Design, or DIY, or just plain using lots of drivers --- that's what it's going to take get you were you'd like to occassionally play at the car audio levels of bass -- which subjectively to me means 125 to 130dB cleanly at the seating position.
If you drop the car audio levels of bass notion than most of these subs discussed in the thread so far will hopefully give you a pleasent experience in sound, (depending on how your room modes and nulls are in relation to your single allowed shelf location. --- But just bear in mind you won't encountere that raw shake your vision/walls/body experience like your car audio memories until you spend more money and allow for much bigger boxes in that size airspace.