Female end on antenna base broke off - what now? Can I attach a shark fin?

I wonder if anyone can help! The antenna mast broke off the base of my 2005. I still have radio signal but it's not as good as it was. I could replace the base, I know. This would cost me $75-$200 Canadian for a used or new OEM base. And I would have to install it (I have seen the installation instructions posted here, they are excellent!). Another option would be to cover up the broken base with a shark fin. Shark fins usually screw into the base. Unfortunately, as you can see in the picture, the female end for the screw was ripped off from the antenna base. Can I connect the shark fin to the green circuit board thing sticking out of the base? I would like to improve radio signal a little. Any other ideas are appreciated.