IANA designer--just had a note to add to the discussion, from personal experience.
A couple folks mentioned the Phil Jones gear as demonstration that deep lows can come from an array of small drivers. An example of deep lows from a single driver would be Mike Arnopol's MAS 110 sub cab. I've got a lot of gig time on his MAS 112 (yes, a single twelve), and more recently an MAS 46/110 stack, with a loud rock band. With a 5-er (Sadowsky Will Lee) into a GK MB800.
Both rigs are light, loud, and low--and amazingly compact for what they'll do. Cheap, no.
To the OP's dilemma: Sounds like the Avatar cab just isn't suited to being the sub in the system.