Since I'm a speaker noob, does anyone have a clue if enclosure thickness/weight/stability/internal space has a roll in THD that's eventually measured?
These factors are not direct contributors to THD, which is a function of the mechanical behaviour of the driver.
Having said that, at lower frequencies the enclosure can certainly indirectly affect nonlinear distortion, but that's mostly to do with its effect on voice coil excursion. For example, all else equal, a ported enclosure will produce the same SPL at low frequencies (from the tuning frequency up) as a sealed cabinet, but with less voice coil excursion. This will allow the driver to behave more linearly at a given SPL, and therefore produce less distortion.
But I don't think this was exactly what you had in mind with your question, right?
Also, is it most favorable to have a speaker enclosure with the least amount of internal empty space?
The short answer is no.. The longer answer is that different woofers require different cabinet types/volumes. Some woofers are designed to perform very well in relatively small sealed enclosures, for example, while others are designed to perform best in large ported enclosures - and everything in between.
But there's no general "most favourable" - each choice is highly driver dependent, and involves different tradeoffs and considerations.
Has 3D printing been a thing in enclosure designs yet?
It's definitely used in parts that go
into loudspeaker enclosures (waveguides, ports, etc.), and I strongly suspect it happens in the portable/bluetooth speaker world, although I couldn't point to any specific examples.