Hmmm... Try giving the truss a bit more tension and see if that solves the rattle.
With dual truss setups it may feel like there is tension when there isn't.
Grab yourself a cheap steel rule from your local $2 shop and with a file, cut slots in one edge that will allow the rule to sit on the fret board, this will show you if the neck is straight when under string tension.

It isnt vital that the neck is on the same plane as the body, infact anywhere up to 9 degree break angle is fine.

With the excessive string height, it is most probably because the nut slots are too high.
Plastic nuts are never a good thing in my book as they tend to be innacurately cut...
You can use the offcut from the end of the string as a file to deepen the slot.
Use it like a piece of dental floss, take a little bit off at a time though, it is real easy to go too low.

If you can post some pictures it would help me to unravel the issue.