About the joystick; the one that comes with Mike's replacement control panel is based on a Happ Super I believe, and has no physical 4-way restrictor. If you want to keep that joystick, you might want to at least get a 4-way restrictor for it from GroovyGameGear.com for $5 (
link).
The Happ Super is marketed as having a 4-way mode, but it is not a physically restricted 4-way mode like a real Donkey Kong or Pac-Man or other original 4-way joysticks had; but rather, it just has a smaller actuator which prevents it from tripping two switches at once in the diagonals. The restrictor from GGG solves that problem.
An even better option in my opinion is to simply buy a new shaft from Mike's Arcade for your existing Nintendo joystick for $16 (
link). The joystick that you currently have as shown in the earlier pictures of your cabinet is a a short Nintendo joystick (for metal control panels) and it should have a 4-way restrictor if the stick is the original and the restrictor isn't missing (this is the same as a Punch-Out joystick BTW; add an 8-way restrictor and it is the same as a VS. or PC-10 joystick).
In any event, all you need to convert it to a proper Donkey Kong joystick is that replacement shaft which will turn it into a tall Nintendo joystick for wood CP mounting.
If you go that route, when you take your existing Nintendo joystick apart to swap the shaft, make sure to clean it thoroughly, paying particular attention to the steel ball and socket in the base that the shaft pivots on. Do whatever you can to get that ball and socket as clean as possible. I usually spray some degreaser in there and let it soak for a while, then get down into the socket with a toothbrush and pipe cleaner. It will take a while if your stick is like most of them; having about 25 years worth of grease and crud in there.
Once you get it as clean as possible, lubricate the ball and socket with something light (I use silicone spray). Heavier lubrication like grease makes the stick feel sluggish when returning to center in my experience. After that it should feel about like a new joystick.