The WP is working fine. The water did exactly what it should have...
I vote that you pull the heads, as the simplest way to see if it's rebuilt (very likely) and how much overbore you have. Then you can put your own head gaskets on and do it correctly.
Get a camera because we will want to help.
Overheating that rapidly is usually not a radiator issue. Have you timed it to the point it get's real hot?
Have you simply taken the rad cap off then started it and see what the water does when it get's ridiculously hot? Does is start bubbling out the cap, is there a crap ton of pressure all of the sudden.