FSS,
The way a shotgun chamber rim depth is dimensioned is not condusive to using and simple measuring tool like a caliper to measure. The rim depth is dimensioned at a "gauge diameter" approximately in the middle of the 55 degree angled rim cut. That is why headspace gauges are used. They are available from Brownells and I recommend that anyone with a lot of guns add them to their basic tool collection. They are used in a set. The "Go" gauge should go in and not protrude from the barrel breachface anywhere. The "No-Go" should protrude from the breachface in at least some areas. Keep in mind that a sxs breachface is not perpendicular to the chamber axis in most cases. The breach face will likely be angled slightly top to bottom.

I used to have the 12g chamber dimension drawing on my computer, but I can't seem to find it. I acquired it from Clymer Tool who makes chamber reamers and gauges. If you buy a set of chamber headspace gauges directly from Clymer, he will send you the drawing free of charge if you ask.