Would there be any problems screwing the ground wire (splayed like a spade connector) directly into the amp in the appropriate slot?

No one around here carries a spade connector that's narrow enough to fit onto the amp, and Im getting tired of looking.

That will be fine, as long as you make sure none of the strands of wire can "stray" over to where the +12v connection is. Make sure it is clean and tidy and you don't have to use a connector.

or dremel the larger spade connectors to thin them down so they fit

I agree with the last two posts. It's pretty simple to make a larger connector smaller. Done that many times. Good luck!

Took SoundQ's advice, and it's working fine...

*knock on wood*