Can this damage to my brake mounts be repaired?
Problem Solvers makes a kit that is usually worth a shot to see if the post is completely shot and needs re-welding:

Cantilever Stud Repair Kit

You could probably even fabricate one yourself if you could find the right tubing diameter. We used these frequently at the shops I managed, and they have a roughly 50% success rate. Having them work properly is largely dependent on ensuring that the base of the original stud is cut and filed very flush and almost perfectly perpendicular to the bolt's orientation.

If you install it successfully, great! You've only spent a few dollars, and you've got the bike back up and running. It's much cheaper than trying to get a new boss re-welded on.

If this does not work, it's only a few dollars spent, and you can explore alternatives.

Installation Instructions

I would not really even recommend trying to have it re-welded, because it's pretty difficult for a welder (unless they're an experienced framebuilder with the correct jig setup) to get the boss lined up to the point that the posts are equidistant and oriented to exactly the same angle. 

Your second best option would be the long-ish caliper brake that RoboKaren suggested. Don't even consider those disc brake adapters; the chances for failure or misalignment (that leads to failure) is very high. Disc brakes are not a one-size-fits-all solution, and require much more precision than those adapters can supply.