i understand your concept, and it might work.
consider though that FM and PM are related. So if you have a source that is FM modulated, and you now vary the resonant frequency of the actual antenna with a tunable reactance, you are adding PM modulation on top of your FM signal (by a variable capacitance in the antenna moving its resonant frequency). Distortions of the FM modulation will ensue, unless you do it very carefully
it IS a sound method though, and has been used before. Like an impatt amplifier...has a limited bandwidth...so add a varactor diode tuning element to the cavity and drive it with a DAC, and voila, you have a virtual huge bandwidth now. The same is used in modern on chip VCO circuits, where they switch in/out fixed lumped capacitances to coarse tune the frequency, and use the varactor to fine tune the VCO.
and on the magnetic loop tuning...i wonder if a ferrite device with a varying DC magnetic bias might work better than a varactor diode in series with the gap capacitance? Might handle a much higher transmit power. the varactor is at a voltage maximum point, and will see huge RF voltages with high power.