The most reliable measurement is with the go gauge (you are sure it is not a no-go gauge?). Snap caps are made smallish so that they fit any 8x57 out there. But to get an idea, add layers of tape to the base of a snap cap until you start feeling it get tight to chamber. That will give you some idea of the chambers headspace. Compare that to your go gauge headspace and to SAAMI specs.
It is very strange that you can not close the bolt on a go gauge. The chamber and bolt might need a good cleaning. I would want to fully understand why the go gauge does not pass even if you can resize brass to fit a short chamber.