Assuming those dimensions are the inside dimensions, I was able to fit a 3" trackball, two joysticks, a handful of admin buttons, and a couple of six button layouts (no room for neogeo stuff, see image below). It's quite cramped though. Personally, I prefer to have a little bit more room between my joystick and buttons.
You didn't specify trackball size or joystick type. The latter is not as big of a deal, but using a smaller trackball (2.25") might allow for a 7th button.
Also, note that the image is just a rough draft of whether or not the parts fit, not something you would want to build.