I have had little experience with subwoofers, so I can't say if this "fullnmess" is just a function of LF content, or not.
I *think* I know whereof you speak. If I'm right, a couple of Timepiece Minis and the addition of an Infra-Wave sub (Bob's proprietary T-line design) will be just the ticket, and I suspect you could secure the trio (aka, the ministers of music truth

) for at or slightly less than your desired budget cap.
I don't know how it compares to an infinite baffle sub design (never heard one, nor have I been in a listening room large enough for one), but IME, Bob's T-line design is far and away the best, most tuneful, most accurate bass I've ever heard. The first time I heard it is the first - and only - time in my music-listening life my jaw literally went slack. It also marked the the
second time I said to myself, "so
THAT'S what I've been missing!"
The
first time that thought ran through my mind was the first time I heard a pair of SP Technology speakers. I guess Dr. Merod and I have something in common, though I did manage to avoid tearing-up.

FWIW, I suspect those who've heard the Revelations will confirm my assessment of Bob's T-line bass, as well as the massive amounts of air it moves.
You want it all, and want it now? Either get the Revelations (or Revelations Grand Masters) for
BIG $$$, or arrange for a pair of Timepiece Minis and an Infra-Wave sub. If what you've written is an accurate reflection of your sonic desires, I can't imagine you won't be thrilled by the results for years to come. If you can stand to have a little less than full-range orchestral output (i.e., your hair won't be blown back), get the Minis first and consider supplementing the presentation with an Infra-Wave at a later date.
That said, I feel relatively certain the "fullness" of which you speak will only be
fully achieved by adding the Infra-Wave to the equation. I'm also certain the Minis will surprise you with their output, but even with Bob's seemingly physics-defying designs, you can expect only so much from the Minis.