Okay, So the FasTrak transponder works on the Golden Gate bridge. I pulled it off the velcro and reattached it at the highest point on the windshield to the right of the rearview mirror. Just moving it up a little bit, now the Richmond/San Rafael bridge will read it. Apparently the increased part of the transponder in the "black dot" area of the windshield leads to better readability.
Since I don't mount my front license plate, the external toll tag is not an option. I did run the "inside the nosecone" idea by the SC. They said they have the same readability problems with that as they do with the windshield mount.