Pulled an audible last week and decided to build a bar-top cabinet instead of just a controller. Started it this weekend using 3/4" plywood (pine?).
Question: Any advice on mounting my joysticks? I'm nervous about the 3/4"... should I plane the wood down? Should I get another board? Should I use acrylic?

Your preference of jstick height is gonna determine which way you go as well as the look. Do you want a clean look or exposed bolts?
If you want full jstick length your gonna have to top mount, which then will force you to use non adhesive graphic covered with plexi.
If you undermount the stick will be shorter, unless you modify with a longer shaft or rebate the bottom(be careful not to go to far), if you undermount then you can use the polycarbonate vinyl.
The problem you will have with the 3/4 is you really have to undermount and use the polycarbonate vinyl, if you plan on using tmolding, across the front.
If your gonna use tmolding and plexi with top mount, you need to plane the panel down to 5/8 so your plexi with sit flush with your tmolding.
So you need to look at those variables and the materials, the look, and feel that you want, which will dictate how you should proceed.