Another completely different way to go about this, and with only one supply would be a Lambda oscillator, plenty of info on the internet about Lambda oscillators.
http://users.tpg.com.au/users/ldbutler/NegResDipMeter.htm
With only two components you will have an oscillator that amazingly will work from low audio frequencies well up into the VHF range.
Connect it to just about any parallel tuned circuit and it will oscillate, and you can then use a digital frequency counter (with very loose coupling) to tweak up all your LC circuits in situ.