zakk, I am not at all familar w/ Apx 24 and these connections, however:
If designed per UG-34 I'd say the "d" dimension is equal to the pressure seal diameter, dim "A" in your sketch, as per Fig UG-34, sketches j & k. I'd say you need to maintain tmin to this diameter. Then perhaps the thickness of the section from A to B would be subject to the thickness under the groove per these sketches. I would take the lip thickness from B to C to be subject to Apx 24 rules.
Alternatively, you could decide the whole thing is a U-2(g) design. Roarke, I believe, has equations for thickness of circular plates as a function of radius, which you could presuambly use. Don't know how or if Apx 24 would relate to this approach.
As to the concentric rings approach I guess you'd equate the deflections and slopes either side of the interface and solve the systems of equations for thickness. I guess. Selecting the proper edge condition could be troublesome. Again, don't know how / if Apx 24 would relate.
Not much help, I'm afraid
Mike
The problem with sloppy work is that the supply FAR EXCEEDS the demand