Just posting a follow-up with my results:

I removed the A-pipe and upon inspection noticed that the inner pipe at the end that connects to the cat was out of center and very close to the outer pipe. It was easy to push it with my finger and make it touch the outer pipe-- exhaust gasses no doubt did the same thing and caused the buzzing.

Note that I could not --see-- any evidence of broken welds. That said, I centered the pipe with a shim and welded the inner pipe to the outer pipe in two places. Removed the shim and it was nicely centered with the 2 small welds not making much of an obstruction for exiting exhaust.

Bolted it back up and the buzz is gone. This was a nice cheap and easy alternative to buying a new a-pipe for my daily driver.

For non do-it-yourself folks, this could be done very quickly at an exhaust shop. I'd just go in sometime when they weren't busy and ask them to remove the a-pipe. You can then point out to them what needs to be welded up. Shop time would probably be about 30 min start to finish.

Hope this helps someone!

Scott