Thanks for the comments, Brent and Woody. I think my neck relief is where it should be, and the aforementioned rattles take into account proper left-hand techniques. I guess I'll just have to get better at "digging in" without causing too much rattling.
As far as action goes, it's .09" on the bass E and .08" on the treble E (thanks to Larrivee's fretboard/saddle design), and I don't want to go much higher than that. I do have a yet-to-be-fitted Colosi saddle handy, though, so I may experiment with that at some point.