If you're hooking up buttons to the U360 directly, yes, you are limited to 8 inputs (not including shifted functions) per stick. That includes the coin and start. If you want more than that, you will have to get a Mini-Pac, iPac or other keyboard encoder.
don't think you can on a re-read of the website. If I could make do with 6 per joystick 1/2 player start and 2 on the side to shift - that might work.
Don't forget the coins. Instead of dedicated "shift" buttons, you can make the "START" or "COIN" a shift button. This way, you free up an input.
Also you can make it so that when you hold down Start and Button 1, you get a credit. Not elegant IMO, but you can have 7 action buttons now without the need for an encoder.