From my experience, it's risky to think in terms of a lumped self capacitance if you want to explore behaviour up towards resonance. It's best to think in terms of transmission line behaviour but even that is only an approximation unless you add more complexity to the model. I've got some old notes and test results backed up somewhere because I tested various inductors using the near field probes and also the VNA. I used a fixed length of wire and used the same bit of wire to make inductors of various L/D ratio. Then I logged the resonance behaviour.
I also looked at trying to make several inductors of the same inductance but with different dimensions. This meant using wires of different length in each case. I do tend to be a bit lazy when it comes to winding coils neatly. My research work was fairly casual here. I am really more interested in commercial SMD inductors and how they (mis)behave up in the GHz region. But I did get good agreement between the various techniques I used. I make VNA measurements on SMD inductors quite regularly for research work. The same applies to SMD capacitors and resistors. The search for parts that behave well over a wide frequency range is a never ending one
It's interesting that I'm testing at frequencies about 1000 times higher than you and Russell and David Knight. I think the same rules apply but the test coils are much easier and quicker to wind in my case. The big impressive coils you and Russell have wound for your Tesla experiments must have taken ages to wind. I don't think I could wind coils that neatly. Was it done in some kind of jig?