Ok, my car is silent with the credit card stuffed under the brace.
I think the obvious better solution would to simply drill a hole thru the thin sheet metal, and put in a machine screw to hold the two sheets together. Put some locktite and a lock washer and good to go pretty much permanently. Now that my driver side is quiet, i do hear a tiny version of the noise from the passenger side. There is a very small space there, I'm guessing about .008 or .012 or so.
looks like i have to take the cowl piece off to get a drill bit in there, but one screw per side should do it.
The sound (on mine anyway) is simply the sheet metal of the brace hitting the sheet metal of the top of the tower. Those tow pieces fit together in a compound curve. Hard to fabricate that exactly. there need to be more attachment points between the pieces. Thus the machine screw.