You said that the gooseneck was bolted to the floor but didn't state as to whether the mic was permanently fixed to the gooseneck, ie the cable going through the gooseneck into the floor as well. If that is not the case and the mic is removable then there are a number of options.
First, to check if the feedback is caused by the attached GN. remove the mic and just hold it gently, this will isolate it from the floor, get someone to jump up and down and see if you still get the same feedback.
Second. Make sure that the GN is not bent too much.
There are connectors and adaptors available that are designed to reduce podium noise and rumble. You can get an isolated XLR socket that will connect to the podium or floor that is basically surrounded in soft rubber. You can also get an isolating microphone clip that can help to eliminate stand-transmitted noise.
What microphone are you using?
Hope this helps. I can give you links to that kind of equipment if you need any more help.