I'm not sure what to tell you about the multiple joint tests. Hopefully someone with experience in this area will be able to weigh in. But your interpretation sounds about right, that the range restrictions in 5.13 would be used to "slice" the range you qualified in 5.12 for the purpose of joint qualification. A min-max method for joint qualification might be sensible, but I can't read it into the code no matter how hard I squint.
On the D1.1 vs. D1.5 testing question, I repeat that it's just a tensile test, a Charpy test, a bend test, etc. Neither the plate nor the testing equipment "knows" it's a D1.5 or a D1.1 test. If D1.1 prescribes a certain test specimen and a certain test protocol, and you have fulfilled that, it doesn't matter that the test also satisfies a D1.5 requirement. For all I know it could also satisfy an ASME requirement, and perhaps a requirement of the Republic of Outer Slabovia Welding Bureau. None of that matters. Test results don't get "used up" by being reported to satisfy more than one code.
Now, if D1.1 requires a different specimen than what you welded for D1.5, that's a different story. But if D1.1 says "take a plate of these dimensions and put in a weld like so and then perform the following tests," and you've done that, then there is nothing about those tests that makes them inherently "D1.5 testing". Put your test results on a clean form that says "D1.1" at the top, and ask them what D1.1 requirements are left unmet.
I couldn't justify taking the trouble to address this in the code. As I said, tests don't get "used up" by reporting them for one purpose vs. another. That would be like rejecting an MTR that says both ASTM A 709 Gr. 50W and ASTM A 588 because there's nothing in A 709 that says that "A 588 testing" can be used. (Then again, there were engineers who used to reject the dual-certified steel, so maybe that's a bad example.)
The closest I've seen to something like this is where different DOTs want PQRs rerun just for them, not wanting you to reuse someone else's PQRs, but that's generally because they wanted to witness it for themselves. That much I can understand; there is a particular requirement (witnessing) that your old test didn't satisfy. But in your current situation I don't think they can point to any unmet requirements. If they can, then there you have it.
Hg