Mike:
Bumper rattles: Push the bumper mounting bracket rubber seal (the one that seals/covers the space between the mounting bracket and the body fiberglass) back towards the bumper a little to expose the outside body where the bumper mounting bracket goes through the fiberglass.
Squirt some clear Silicon Caulk all around the bracket where it passes through the body such that it is forced into the space between the body and bumper bracket.
Get under the car, and squirt more silicon in from the back side around the bumper bracket, the same as you did on the front. Make it look neat.
Back on the outside, use your finger to make the silicon around the mounting bracket look neat, then slide the rubber seal/cover back into place such that the silicon will "glue" it back in place so it won't move. Hopefully, you don't put so much silicon caulk in that it squishes out all over the place when the seal/cover is replaced. If you get a little squished out so that it shows, you can either try to remove it now, or wait til it firms up and carefully use a sharp razor blade to score it along the seal/cover and just pull it off.
Leave it be for at least 12 hours to allow the caulk to thoroughly firm up all the way through.
Do this to all bracket locations where the bracket goes through the fiberglass. Once this is done, your bumper rattles should be eliminated.
Do the bumpers first and see if that cures it. Bumper rattles can sound like they're coming from all over the place, so try this first, then report back, eh?
Body Rattles: Don't go the rubber-between-body-and-pan just yet. First, try tightening all of the pan to body bolts all around the bottom, including those out on the back, just ahead of the shock towers. Bruce mentioned the front body bracket - find that one (it should be right ahead of your gas tank) and tighten those four bolts, too. Let us know what happens.
While you're under the body messing around, look for anything (wire groups, hoses, brackets, etc.) that is on a torque arm (set at a distance from its' mount, thereby making a lever) that might be moving around when the car is moving. If it moves, tighten it. If it still moves, find a way to keep it from moving.
Another common "body" rattle is where the Speedo cable goes through the fiberglass to enter the cockpit. Use your new-found silicon caulk trick around the cable where it passes through the fiberglass. I'll bet you'll find several places to use that tube of caulk up. Good hunting!
Good Luck, eh?
gn