For all the work you will be doing to your car you should not stop at the pulling the cowl and fixing the problem properly. To anything less is half a job.
Odds are you need a new window seal anyway if you have the old one.
Buy a good spot weld drill, the mill kind not the circle cutter kind. Spend a day drilling spot welds and then build up the new inner parts. The cowl practically self locates, but just be sure by drilling a few holes for screws before you take it apart.
I did it on my fastback. I scared to pull it off not having a clue what I was doing at the time. Turns out to be pretty easy to do. I even made up all the inner cowl stuff from scratch. In the end you will be glad you did.
There is one other fix, but it will only work on minor cowl problems. Some have cut open just the end where it is hidden by the fender.
Any other cutting and welding back on would be more risk and work than just doing the spot welds. Too much chance to damage or warp the top of the cowl.
Just keep in mind you are about to spend some significant $$$ trying to make a classy car. Fixing the cowl vent is very cheap, mostly just your labor. I did mine for the cost of two bits on circular spot cutter plus the cost of the mig welding. The metal was picked from the trash, a microwave oven.