The idea of using bifilar conductors essentially creates the conditions of two long skinny capacitor plates. Things get kind of wonky though when you start wrapping these conductors around a form, i.e. the interwinding capacitance is all over the map. Some turns are tight against adjacent turns of the same conductor and others are tight against turns of the other conductor. It's so hit-or-miss and very hard to duplicate.
If the two bifilar conductors were first twisted together, then wrapped on the form, I suspect you could get capacitance between the two conductors that are fairly consistent.
It's that capacitance between conductors along with the inductive properties of winding around a magnetic core that determines the self resonant frequency for the coil.
My feeling is if one were to use unshielded twisted pair (preferably magnet) wire, where the conductors are very close to each other and have an outer jacket that is relatively thick, you could wrap this cable on a bobbin, insert a core when finished and do it multiple times having the self resonant frequency of the coil assembly be with 5%--very repeatable. Then it would be just a matter of choosing the proper core and wrapping the bobbin with the proper number of turns to get the desired resonant frequency.
There's a lot of talk about what resonant frequency is necessary for splitting water. I have no idea what to make of that, but I do know with the right procedure, we could make coils for any of those frequencies and find out what works and what does not.
There could just be a lot more to this mystery we don't understand. It could well be that you need particular harmonics up into the GHz range that makes water splitting possible. That's actually my gut feeling about it--some sort of travelling wave moving at a particular velocity factor, traversing a particular length of conductors. And if that's the case, how we build our coils gets a whole lot more difficult.
In any event, we need a method that is repeatable. If it fails, then hopefully we learn from our failure and try something else.