I'll take a poke....
Depending on the frequency range a sub is going to cover it may have some effect in terms of localization. As you get up over 60-70HZ it becomes easier to locate where the signal originates. You are also moving the output source closer to a room boundary when using a down firing design. This is going to have different effects based upon every room... also based upon where in the room you listen. There are disadvantages in terms of unwanted noise (hisss.. or hum) that may originate from a sub and in those cases where you might have a slight background noise it may be more noticeable from a front firing design rather than a down facing driver. You loose a teeny tiny bit of excursion due to driver sag in a down firing design but it is pretty much negligible. You could claim that the driver stays better centered in the gap since gravity isn't working against one side or the other. I don't know.... it doesn't seem to make a difference either way as long as it is a good quality driver.
My final analysis of the debate front vs. down firing is that there are plenty of good examples of musical subs that use both methods. ACI has the Titan, which plenty of people find very good at music and REL subs are universally accepted as musical designs. Both use down firing drivers. I wouldn't say that they sound good because of the fact they are down firing though.... the engineers just used good well-known techniques to build a musical sub, same as we are doing.
In terms of phase... you can change that easily enough. Also, at these frequencies phase differences are not easy to discern. The size of the wavelength helps with that problem. I won't argue that multiple subs are not a good thing. Just buy two!

Two or more subs will even out in-room response by exciting more room nodes (not by causing fewer).
On the distortion argument we will win against anything close to our price point. I'll let Tom Nousaine report on those types of arguments because they are easily handled by measurements and nobody needs me to blow smoke about a subject untested by a third party.
In terms of box size it doesn't have so much to do with distortion as it does efficiency. Wiggins is fond of mentioning Hoffman's Iron Law. Don't quote me but I think the three variables of box size, power and extension at a given spl are all you have to play with. If you make the box smaller you have to increase (or decrease) one of the other parameters. Small box mean lots of power to get the same output at a given frequency. Of course you have to design a driver for a given application. If you put the Tumult in a huge box your still going to need a fair amount of power to get it to full extension. If you use the Tumult in an Infinite Baffle application (very large box) you get less of a pronounced hump as seen in our response graph with more low end extension and it would require less power. When you put it in a smaller box your frequency response hump raises such that you get less low end extension and you require more power. You can EQ the response but that isn't free.... it requires more power. None of these really relate to distortion. That is more a function of the driver and how closely it operates in relation to the input signal.
If our design goal was a large subwoofer it would allow us to use a different driver with lower power requirements and we could achieve the same output for less money (unless you consider box cost and shipping). These days high power Class D amplifiers are cheap and Adire has advanced the art of motor design so that we can get high excursion drivers with low inductance, very low motor based distortion & power compression. Those two factors (XBL motor & high power amps) are what allow us to produce a sub that has more musical output than anything else available in this size. I'm sure other companies will pick up on this.... we are just small and quicker than the big guys.

Also it doesn't hurt to have family connections.