This is a useful tool for some context:
http://www.baudline.com/erik/bass/xmaxer.html
A single 18" driver would require an Xmax (linear excursion, one-way) of 23.7mm to achieve 105dB@16Hz.
If it was my project, I'd go for a pair of Faital 18XL1800 in a cube. Go for force cancellation. Then, find the biggest amp you can find and bridge it. My current favourite is the Powersoft T-series amps. I'd probably go for a T602 or T902 here. Old iron amps are cheaper, though. A pair of Crown MA5002VZ would be fun, but you run back into the weight issue. That, and powering the damn things.
NB - the above applies in groundplane conditions.
Things change, of course, when room gain is considered. My current listening room is incredibly helpful in the bass. With a pair of speakers which are rolling off (-3dB) at 50Hz with a 12dB/octave slope, my room gain gets me to a +15dB mountain at 40Hz, and the response is back down to nominal level at 10Hz. The speakers themselves have 2x 8" drivers each, which is enough for tactile bass if the recording supports it.
Given the approx. 20dB of "help" that my room gives, that's equivalent to having 10x the number of drivers if I wanted the same experience outdoors.
My conclusion, then, would be that given how unpredictable rooms can be, it's best to measure what yours is likely to do before trying to choose something to do a job. You could literally end up an order of magnitude out.
Chris
PS - I wrote this:
https://www.prosoundweb.com/spec-wars-looking-inside-loudspeaker-spl-specifications/ a little while ago, after arguing with some sales guys that their posted specs don't even pass a sanity check.
