Quite an interesting discussion...
At work a couple of years ago, I built an autotuner to match a PA to a coil/antenna in an NQR (nuclear quadrature resonance) "substance" detection system, which worked across much of the LF and HF band at a 100W class power level.? Used an AD8302 and did just this:? measure the complex coil impedance at the desired frequency, select the best available components for match, and iterate twice.? As mentioned, the parasitics affected efficacy.? Since this was a feasibility project with a short turn time, we performed a calibration procedure, which worked well for a one-off (or few-off).? It was very much fun.
Given the chance to refine, which might actually happen soon, I would go with at least one continuously variable element (e.g., small vacuum variable with associated motor and drive).? The application does have SOME SWaP (size, weight, and power) constraints...
Todd AG4AY