You start good and interesting with some valid points.
The problem with using obscure law of war and ideas that Washington DC is not part of American law is that it doesn't pass with the public or other groups. Those systems are designed to only work one way, so that obscure provisions can be used to withhold information or turn down prosecutions/investigations. Imagine being a prosecutor told that you have no authority because DC is French (or something like that) - you can go to a newspaper and they might print it …. But it's not going anywhere and you get harassed by gang members who are being paid by intelligence agencies.
Those systems are not designed to allow you to launch investigations using them - much less to actually be pursued as a legal recourse.
At best, you could use good actors to get information out of them that could be used later in a public court - but if Trump were to be bringing up law that came out of the Vatican to try and hold Hillary to it - she would obviously have no obligation to be held to it. It's like asking for a guild of theives to behave honorably while you act to investigate them for theft.
You may as well hand the taliban a list of our people and ask them to help us get them out. Maybe a few of them are going to honor that - but you're talking about a group of militants who have been opposing our presence and killing us in the past. I'm sure they'll abide by the terms and conditions as long as they are getting what they want … And just ignore the parts that are inconvenient.