Has anyone had to weld part of the anti-sway bar mount attached to the motor frame? My driver's side mount is busted. I'm hoping I can just weld it instead of replacing the whole assembly.

I wouldn't weld it, if you understand the amount of torque travelling through the sway bar, it is not something you should weld, it would only be a temporary solution at best.
Welding can also induce material deformation through the heat of welding which could adversely affect the cars track and handling.
Rather be safe and replace the assembly.

BTW, exactly what model car are you driving?

I drive a 1997 Subaru Legacy Brighton Model (wagon) AWD. Thanks for the advice. Any web site suggestions for that part?