I don't see meeting all of your wants at once. In wall speakers are a possibility, though. I will mention that most small speakers with their poor directional characteristics is going to make intelligibility a problem. In a room with high ceilings and reflective surfaces, you need absorption and diffusion along with highly directional speakers in order to get a good direct sound to reflected sound ratio, IE: clarity.
Chest pounding, hair raising bass is going to do nothing for you other than attract unwanted attention from your neighbors, possibly the HOA and / or law enforcement. Proceed at your own risk.
Cheap and good are mutually exclusive when it comes to low frequency sound reproduction. If you can live with a higher F3, then pro sound drivers are going to be your best bet. Higher efficiency, though shorter xmax.
As an example for a sealed box, keeping cone area constant and the same SPL, each additional octave lower cone excursion quadruples. From 40 hz to 20 hz would require 4x the cone excursion, dropping it to 10 hz would require 16x the cone excursion compared to 40 hz.
Cone excursion calculator here: http://www.baudline.com/erik/bass/xmaxer.html
A single 18" driver in a sealed box called upon to provide 121 dB @ 20 hz @ 1 m would require ~ 95 mm excursion one way, an impossibility. Dual 18's in a sealed box would require 47.5 mm one way excursion, or 95 mm p-p, also an impossibility.
For "live" levels, plan on at least 110 dB at the seats. Sitting ~ 3 meters away from your wall, you will lose about 9 dB from doubling the distance from your source. 110+9 = 119 [email protected]
1 m. You may gain 3 dB at 20 hz from boundary placement, lowering your requirement to about 116-117 dB at 1m.
Using the calculator, solving for number of drivers, plugging in [email protected]
at 20 hz, results in ( 6 ) 18" drivers, keeping excursion to 10 mm one way, 20 mm p-p.
Even capping output at 110 dB @ the main listening position, which would be at least 11 dB below reference level with redirected bass, requires a lot of drivers and excursion. [ 6 18" drivers moving 10 mm one way or 20 mm p-p ]
To reduce the number of drivers and amplifier requirements I would suggest a ported enclosure. Ported enclosures require
a high pass filter below tuning to protect the driver from over excursion. An amplifier with built in DSP would be best to integrate with the main speakers, providing for a high pass filter ( required ) and allowing equalization and delay functions.