So I built this tool to resurface the seal surface inside the radiator. And it worked!
Step 1: Turning the Tool on a Lathe
The dimensions will vary from car to car. The smallest part needs to just fit inside the inner hole in the radiator inlet. The step needs to be flat, and the middle diameter needs to fit just inside the top portion of the radiator inlet. The large outside diameter is just to hold and turn with.
Once you've turned the tool, you glue sandpaper to the surface of the step. 200 Grit is probably good, although you may need finer grit to get a better seal. No worries, you can just glue another piece over the piece you already glued on.
Step 2: Resurfacing the Seal Surface
This helped my problem a lot. While the cap doesn't quite seal at the right pressure, it doesn't have a hole now which helps a lot. I'm going to add a small piece of rubber from a bike tire probably to increase the thickness of the cap and make up for the removed material.
Honestly, if you can afford it, just go buy a new radiator. But when you are working on a $450 car (like mine), a new radiator is 20% of what I paid for the car :)
Step 3: Improvements
I didn't realize how fast it would work, so I would use some finer sand paper to make a better sealing surface.
Originaly I was going to lathe down the other end so you could just chuck it in a drill and go faster, but I have a mini-lathe and it took quite a while to turn down the tool end, so I opted to just make it hand powered. Which worked out great, and prevented me from taking off too much material while re-surfacing.
So, round the sharp edges, use finer sand paper, start with a thinner piece, and turn down other end so you can use it in a drill.