If you haven't cut the wood yet, select the joystick that suits you best and alter the plans a bit if necessary.
If you have 2.75" clearance under the panel, that should be sufficient for most joys unless you go for a rotary, 49-way, or analog trigger.
If a restricted 4-way is what you want, there are a few choices that don't take a lot of room under panel: a Ms. Pac Reunion, a j-stik, mag-stik, wico, etc.
Check
Happ joys for exploded view to give you dim's.
Some at
GGG.
For j-stik and mag-stik see
Ultimarc.
Diagrams..
For a Wico, check ebay or post in B/S/T here.
There are also Sanwa, Seimetsu.
An inexpensive 4-way option is a Happ Super with a restrictor (see
GGGTornado Terry's has Ms.Pac joy and others
TTDivemaster and ponyboy in B/S/T may have some options.
If you do a search here, you will find many threads regarding 4-ways.