I would use an inside micrometer to find the ID. The jaws span the thread peaks and give a better reading. The problem is that you probably don't own one of these contraptions so the next best option, for me anyway, would be to take a piece of round stock and turn it down until it juuust slips into the bore and measure that. We know that production tolerances for threads can be rather coarse so we cannot rely on a standard; using a plug gauge you make would at least get you within a few tenths if you work carefully. Then you'll at least have an idea of what the minor diameter is. Then you can sort out the pitch with a pitch gauge and you'll have your thread.
It's going to be fun sorting out the thread form. I'm not a gun guy but figuring out if they used a 60 degree thread or a 55 degree Whitworth could be challenging to do by eye. Here I think the Cerrosafe stuff might come in handy.