@corbo, no problem, and the LS-56 does have octagon gates available.
Personally for undermount quality, feel, flexibility and minimal depth I would go with the JLW, for a few extra dollars you are getting 10x the stick.
If you are going to recess, I would go with an LS-32-01, they come with a plate that is very well designed for a 1/4 recess while providing a flange so you can undermount into 3/4 wood.
However, form factors are important, let me know if you need any more dimensions and I'll be happy to measure them for you.
I will clarify a few things:
Ignoring the other incorrect measurement of our Spitfire™ stick in this thread,
"our Spitfire™" joystick is one that has been offered by at least 4 other vendors for over a year. The Fight Stick 1 and Fight stick 2 are the same stick with a PCB for micros that we have been selling since March of last year. The name is really cool, but this is a generic stick.
The two dimensions are so close on this model due to the protrusions on the restrictor plate, apparently there to ensure that there is no interference with the shaft when in operation. These posts can be ground down, but the restrictor retainers are just about as tall. Realistically, the "B" dimension doesn't have much importance, as the shaft needs to have clearance to move freely, and there are often other parts and protrusions which make up the body of the joystick below the switch level.
This is an interesting theory, however if you look at the Sanwa stick (a stick we also carry), which this is a copy off, the tabs near are used a retainer for the 4/8 way restrictor ring, to lock it in and allow you to turn it. While they may serve a dual purpose, my guess is that they are probably just trying to imitate the original for cheap. Some people tried to sell these sticks early on as Sanwa's and as 4/8 way switchable, but they are are neither. These aren't bad little sticks, and actually these sticks with an octogate restrictor is a great solution to have 8 way and 4 way games play really well without changing the restrictor.
I think the biggest question in my mind is whether you will be mounting in a wood or on a metal panel. Few of the "Japanese-style" sticks are well suited to below panel installation in wood, and as a result, can get much smaller based on the way they are usually mounted. They all get a lot shorter if they end up embedded in the wood, which is pretty much a necessity with this style.
This is a great point and actually the Seimtsu SS mounting plate allows you to do this while providing a flange so your mounting bolts can go into 3/4 wood. This is nice if you want to avoid through holes and doesn't bolt into the thinner and weaker recessed section. These mounting plates can be put onto Zippyy or Seimitsu brand joysticks, both of which will take 6mm threading.