Tuning an LC can be done in a continuous fashion using feedback... add in a SIGNED (or variable phase) percentage of the tank's output, see...
But observe...
(1) E1 will (in this case) need to be about a 10W amplifier... but not a particularly difficult task at 100kHz
(2) Clever souls will realize that you can automate this feedback by adding a PFD to compare between driving function and phase of tank output.
(3) Likewise control of output amplitude and Q can also be automated. ...Jim Thompson