For room correction for the subs, would a Minidsp 2x4 be enough or do I need the 2x4 HD?
I would not use the unbalanced 2x4. The preout voltage is too low. I have successfully used balanced 2x4. 2x4HD allows longer delays and has standard voltage on the RCA preouts. It is also marginally easier to use if your processor or subs only have RCA inputs. No need to cut cables and make sure they’re wired correctly into the terminal.
Multisub for room modes doesn't have much benefit unless you want to seat 5+ other audiophiles in a theater and have heavy bass trapping in the room.
Quite a feat of rhetoric there: internally inconsistent, yet on its own neither piece makes sense!
a 12" driven/12" passive radiator sealed subwoofer(s), with an equivalent area to a 17" woofer - or double 10" driven sealed subwoofer(s), with an equivalent area to a 14" woofer. Cabinet vibrations should be lower as well, as the subwoofer(s) simply have more weight.
Careful there.
First, as others have explained PR is the functional equivalent of a port. It does not increase volume displacement. It does increase efficiency over a narrow bandwidth, and decreases efficiency below that bandwidth. As discussed, the advantage of PR over port is no pipe resonances.
Also, all else equal a PR sub cabinet will vibrate
more than a closed or vented box. The reason is the movement of the heavily mass loaded PR cone.
King of subwoofer is horn by the way. But a true horn loaded subwoofer takes a lot of space.
I would say the opposite. Horns (inasmuch as any device that fits into a small room and outputs these long wavelengths can accurately be named “horn”) are the
absolute worst for deep bass. The bandwidth limitations are crippling, and resonances above that tiny bandwidth are staggeringly bad. There is also limited ability to pressurize the room below cutoff. Theoretically the best solution is the common, humdrum one: multiple closed boxes. Smoothest frequency response (in passband
and above), strongest deep bass (can excite modes below nominal cutoff), sufficient efficiency. While your big black eyesore above may be cheaper to make (fewer drive units to buy) and lighter, I suspect there is no way it will outperform multiple closed box woofers in the same volume, even if collocated. From a marketing perspective there is no gobbledegook one can craft about such a basic subwoofer design though.
Build your own subwoofer(s) and you'll have premium parts compared to most retail subs, and save a fortune.
That only holds by ignoring the price of your time and capital (tools, workspace), and are either an accomplished woodworker or willing to accept sub-professional appearance. If you subcontract the build to a commercial artisan you will invariably pay much more for equivalent performance. However, you will also get subs that are designed for your space. Politically that can be helpful because all relevant actors can have a say in the shape and finish, thus giving some measure of buy-in. Practically that can be the difference between subs in the room and no subs.