Thanks, all, for your comments. My response was delayed because I decided to have a local shop look at the problem. The problem was not the header (~3/8" clearance), but contact with both the trans mount and diff housing. The motor, trans, and diff mounts have only a few thousand miles on them and look solid.
To solve the problem, he bent a new 2 1/2" exhaust system, installed new hangers, a 24"-long resonator, and reused my DynoMax Super Turbo muffler in the back. What a difference. No more rattles, and no more resonance at 1800-2k RPM! I'm very pleased. I also had an O2 bung installed in the wye-pipe for an aftermarket FI system still in the research phase. I attached a couple of before & after pics.