It looks to me from the streaking on the fretboard that it may be dyed rosewood. If so, no biggie, plenty of guitar companies use "ebonized" fretboards. The "dip" in the headstock is a little wierd... sanding error, perhaps?

The real Supremes are supposed to be chambered, and while feedback resistant, are definitely not feedback proof.

I suspect the cause of your setup issue is the nut was cut way too high... Any problems with fretting notes on the first three frets?

Like most that have bought Chinese "Gibsuns", a new nut, setup, and electronics will turn 'er into a player.

Keep us updated on what you decide to do!