Do you ride stiff boots? If so they'll restrict you from laying the board down flat putting you up on edge. If not, make sure you're not jumping too high when spinning. Keep it low and push the board down flat base when you land. That's where I'd start. If you're still having trouble you could try a 3 degree base bevel to get the edges off the box.
Everytime I try to spin on a box I catch an edge and eat major shit. How can I spin without catching edges.
I can 50-50 to boardslide, boardslide, 50-50, 180 on and off, blah blah.
I can 360 and 180.
One of the easiest ways to spin on a box is to just hop onto the box using a 270 on spin onto the box and just stay relaxed and continue to let your body follow the rotation around.
You'll naturally keep spinning as long as you keep continuing to look through the rotation.
Don't try to force rotation when you're already on the box, the key is hopping on with enough rotation to just sit there with a flat base and let the rotation do all the work.
Since you said you have 360s down, the 270 on portion should be no problems, then it's just a matter of going with the rotation once you land and keeping that base flat. That's how people spin 540s, 720s and more on boxes (super fun on a long box if you get the line right and stay on until the end).
ps - besides all this, make sure your edges don't have burs, that can cause catching sometimes.