I think you probably could very carefully repair this with epoxy and maybe some additional metal or plastic.
In the long run you may be better off letting Sony fix it. Home repair will probably kill your warranty.
If warranty is out, I would definitely try an epoxy fix. And a mod to strengthen mount.
EX3's have the same problem. With those you can get a plate from:
http://shop.dm-accessories.com/products/ex3-plate
or
http://www.vfgadgets.com/grip-camera/ex3-heavy-duty-base-plate-system
Maybe someone will come up with a plate for EX1's, I have thought about making one. It is not as easy as for the 3, and it would need some modification of camera body.
If someone in my area, NH, has an EX1 and wants to try to improve base get in touch with me.
Olof Ekbergh