The article you referenced does indeed have some useful information for achieving the Vox cosmetic look. I'm sure you've noticed that the referenced cab's dimensions are not the same as the one you listed in your earlier post. I presume the one in your picture is the so-called 'T-100' cab and the one in the drawings is actually a Super Beatle cab, which is taller and shallower, but essentially has the same internal volume. As previously observed, you don't really have the internal volume you would need to get adequate bass response out of 4 drivers, but I gather you're determined to go ahead with the concept. Have you determined what driver you're going to use? Four of anything worthwhile adds up to an appreciable amount of money; it seems a shame to stuff them into a too-small enclosure, but hey...it's your project. Is there some reason why you decided against the Vox 215 concept? There's not really enough volume for that either, but it seems like you'd be closer to it.
Circling back to the construction article you referred to: simple reinforced butt joints would be sufficient joinery -- don't let his digression about dowelling or dovetails distract you. Your carpenter will probably tell you that. And you certainly don't need to reinforce the corner joints with steel angle iron, another technique the author endorsed -- not unless you're going to be suspending an interconnected column of these things about 8 high.
The OP wants to do a 412 configuration, so it isn't quite that simple, even if it isn't particularly complicated. If you want the cab to be 8 ohms total, the only choice will be a series/parallel combination of 8-ohm drivers. For a 4-ohm cab, you could use 4 x 16-ohm drivers in parallel, or as with the 8-ohm cab, 4 x 4-ohm drivers in series/parallel.