I read the original post you linked to. It sounds like you still do not know the dimensions of your current chamber. If you did you may find you have more than "very limited options" for a simple rebore and rechamber.

You could do a chamber cast. Alternatively, you could fire-form an 8x57 case to the current chamber by loading and shooting a wax plug instead of a bullet. Who knows, maybe something as simple as .35 Whelen or .338-06 might clean up the chamber. Either of those could be loaded to an OAL to fit the action. But you need to know more about your current chamber to find the proper solution.