How would you fix this cowl rust?

My 1964 Valiant is a solid CA car, but for some years there has been a leak on the pass. side that rusted out the floor. I am repairing the floor and wanted to find and cure the source of the leak. I assumed it was the wiper pivot or the windshield, but nope, it was a blocked cowl drain. The cowl itself seems solid, I poked and prodded as much as I could. The only damage seems to be the 'dam' that keeps water out of the passenger vent/heater.

Problem is, now how do I fix it? I'm not sure I can get my MIG gun up in there, much less an angle cutoff wheel...