I have J-stiks mounted approximately 2/3 of the way through my MDF panel (or about 1/4" of wood), held with carriage bolts. It is very solid, and I seriously think the joysticks themselves would break before the wood would break, if someone where trying to break something (MDF isn't particularly strong in some ways, but the "grain" is going across the surface which makes this practically the strongest way to use MDF).
As far as the stick height... there are lots of joysticks that are used in wood panels in the original, dedicated cabinets. The height of the stick varies between pacman metal CPs, fighter metal CPs, and wooden CP's like Joust/robotron. So I think stick height is really a personal preference (I would actually prefer my sticks to be slightly shorter).
That said, for anyone who is concerned about the strength, I think Grasshopper's idea is a great one. With a thick plate, it would eliminate ANY concern about the strength of the joystick mount in wood, when used with carriage bolts through teh 3/4" portion of the panel. It would also give us a way to use pacman sticks on wooden panels, without top mounting or a visible plate (could leave "just enough" wood, like 1/8"-3/16").
Wade