If you had a wall enclosing the area to 3m wide x 3.8m x room height then you might be able to get away with a smaller and less powerful sub. The thing is though that your room is open plan. The room's volume of air determines the sound pressure that can be generated within it. The bigger the space then the louder the system (sub in this case) has to run to create what we perceive as a decent level of sound.
There's nothing to stop you using the MRX10 in your room, but I'd be surprised if the driver didn't end up bottoming out if you're listening at enthusiast levels. It's easy to turn down a sub that too big for a room, but impossible to make an under-powered sub do the work of something better.
According to some stuff I've read, the Double Gem is about on par with the XXLS400. That makes sense. BK had had requests for a sub with XXLS400 performance but that would fit in the floor space of an XLS200. That's pretty much what the Double Gem is.
The Mass W200 sub uses 200W (peak?) amp to drive a 10" long throw* driver. It is complimented by a 10" passive radiator. If you're not sure what that is, from the outside it looks like another bass driver, but inside you'd see that there's no magnet and driver coil assembly. It can't be connected to a power amp; hence it is passive.
With a single bass driver, when the sub driver is moving in the opposite direction to the bass cones in your Tannoys we'd call that 'being out of phase'. The result you'd hear if you left it like that is weak bass because one movement cancels the other. This is why subs have a Phase switch on the back.
In a sub or any speaker with a passive radiator, the air pressure inside the sealed cabinet causes the passive driver to move in the opposite direction by roughly the same amount. In this way, the acoustic effect of main bass cone moving backward is counteracted by the passive radiator moving forwards. There's always a positive movement of a bass cone going forward.
Passive radiators aren't a complete win win solution though. Because it's not driven, the bass pulse isn't as strong as the main powered driver pulse. For that reason, the contribution from passive radiator is counted as ½ (half) compared to 1 from a driven speaker cone. Also, for a passive radiator to work, the speaker can't be a bass reflex unit for the powered driver. It has to be a sealed chamber. Bass reflex gives the designer the opportunity to get more 'thump' from a given size driver/amp/box combo. But it's at the expense of speed and tunefulness. However, make the cabinet large enough and use a big enough driver and potent amp then the limits of a sealed design are largely outweighed by the benefits. That's what (IMO) makes the BKs so popular. Their performance punches well above their price point.
The story with the bigger subs is about having one large box capable of pressuring a room. The larger the box and amp then the bigger the driver; and the bigger the driver then the more air it can shift. But there is another way...
The Double Gem uses two 10" drivers. These have combined surface area as one 14" driver. Although a 14" driver will go to lower frequencies, it's much harder to power it, it needs a much bigger box, and it's harder to keep the bass from it tight and tuneful. If you're trying to pressurise a large area but not so bother about shaking the foundations of the building then two smaller subs could prove to be far easier to accommodate. This is along the same lines of thinking as BK. They did tests with two Geminis (10", sealed box, 150W RMS rather than peak power) and found the results very similar to one XXLS400. That's how the Double Gem idea was born.
Geminis also have a very clever dual input crossover. This lets them work at speaker level fed directly from a parallel speaker connection at the amp that draws no power, and at the same time they can run from the LFE output of an AV receiver. In effect, that's like upgrading your main speakers to something with 10" drivers and having a subwoofer as well.
* Long Throw drivers move more air thanks to the larger cone excursion on each bass pulse. This tech has been around for quite some time.
(all in circa £410 so £20 more ish..)