Thanks to m38inmaine looks like we have an answer to the Goat issue. He found a thread with a description of exactly what it's currently doing and how it would have gotten to that point.
~"Had a tired old 3-53 in my backhoe (rest in peace). I second the notion that these motors just keep running, long after they have excessive wear. FYI, these motors do not have a "head gasket" in the sense you'd be used to on a regular engine. There are lots of orings under the head sitting on top of the block that can be damaged if the engine is overheated. Also, this motor has pressed in sleeves of the "wet" variety. The coolant surrounds part of the sleeve, and there are large orings to keep the coolant from getting into the crankcase, or air box. These also get trashed in an over heat. Good news is, an inflame rebuild kit is darn cheap compared to many other diesels. It'll come with liners, pistons, and all those afore mentioned o rings. There is a small pipe on the side of the crankcase, that points towards the ground. See if any coolant is coming out of it. That's the air box drain, to let condensation drain, but if it has coolant coming out you probably have toasted orings."
So while it is a serious issue it's not insurmountable. After changing the radiator I don't really relish the idea of pulling the head but it beats pulling the engine.