Speakers in small boxes can be made to have response that is reasonably flat and low, as long as the box is tuned appropriately. Check out the alignment called "Underdamped Ported Alignment, tuned low". That particular response curve was made with a rather large box, but you can get a similar response curve in a small box with appropriate tuning.

More likely is the case shown as "EBS Stepped Response from ported cabinet with specific peaking", which is attractive since your Dayton motor will be used fundamentally in its lower stepped region, which is flat. You can crossover before the edge of the step where response rises. Granted, this is a lesser efficient part of the curve, but it is a way to get flat response over the intended range from a very small box.

For that matter, you can generate an "Overdamped Ported Alignment" using certain tuning in a undersized box. This isn't what you would want for a subwoofer that would be used in large rooms or outdoors, but it is perfect for home hifi use, for subs that will be used in small to medium sized rooms or when corner loaded. Room lift tends to boost the lowest frequencies, and this kind of response prevents room gain from forming a peak.

A 3.5 cubic foot sealed is very similar, having -3dB at 30Hz, -6dB at 24Hz and -12dB at 17Hz.

Your proposed 2 cubic foot box is too small for sealed because it becomes underdamped. Not too badly though, so I wouldn't consider it to be unacceptable. A sealed 2 cubic foot box gives a -3dB point of 30Hz, so it is similar to the larger 3.5 cubic foot box but underdamped.

My suggestion is that you build the PiAlign recommended cabinet, and that you consider 3.5 cubic feet a minimum chamber volume. If you must run the system in a 2 cubic foot cabinet, you should tune it as low as possible or just leave it sealed. In a cabinet this small, there is nothing you can do to prevent the system from being underdamped.

Can you explain this whole concept of damping? Underdamping, overdamping, what do those terms mean, exactly?

Adam

Notice that the examples of resonators each have two reactive elements. The mass and the spring are two reactive elements, the electrical circuit has an inductor and capacitor and the Helmholtz resonator has mass of the air and its compressibility, just like a mass and spring.

If you add a resistance, you are providing damping. A shock absorber of a car is a damper, and it prevents the car from bouncing wildly at resonance. Likewise, the acoustic/pneumatic properties of a loudspeaker cabinet control the resonance of the speaker.