I went with JB Weld - $5.00 for the pack; 5 minutes to apply it.
SS double sink @ defender: $699 and - what - at least an hour (totally optimistic) to install. Let's see: $5.00 and 5 minutes... $699 and at least an hour...
Yup, I think I made the right decision. And if it only holds for a few months, then I'll have another go at it.
As to how that hole appeared... Now that's a good question. Only thing I know: I store a rubber mat (which I place washed dishes on) in that section of the sink and the result is that there's often some standing water there. But I can't see how that could cause a hole to form. But maybe it did. Maybe those with more expertise than I have can answer that question.