Best substance to repair broken shifter

My vote is other - cash.  Replace it. 

Don't waste your time.  Super glue and/or epoxy will not handle the forces applied to a bar end shifter and if it did work, I suspect you'd make it about 15 minutes before it eventually let go.  Additionally, its a white-metal casting, so there's no way to weld it - bite the bullet and either find a used/new set.

-John

Call/email Shimano customer service. Tell them what a fan you are of their product and the circumstances behind their product failing. You might just get a new one free of charge.

Contrary to popular belief, customer service isn't dead. I recently contacted the 5.11 company to inquire how I could purchase a new set of temples for a pair of sunglasses I own. They told to simply email my address and they would send me a new set of "frames." 1 week later the Big Brown Truck left me a package on my doorstep containing a brand new pair of sunglasses and an accessory package. I was prepared to spend half the price of the glasses to get replacement temples but got pretty lucky I guess. It's worth a try, they are Dura Ace for goodness sake!

-Chris