oscillators get their "goodness" from how decoupled they are from their loads. So by design one often deliberately sacrifices output power for more stability by decoupling the oscillator from the load.
In your case, maybe a series reactance between the oscillator and antenna input helps to do that.
BUT, if the frequency determining element of the oscillator is the antenna itself...then the oscillator's frequency, noise, output power, etc will be STRONGLY determined by what is near the antenna. For instance, put your hand near the antenna, and the frequency moves.
so a test might be how much the frequency moves due to loading effects. You could hook up a horn antenna 4 inches away that has an attenuator (like 3 dB) and then a sliding short, and move the sliding short around and see the +/- frequency change. You could use the same setup with a directional coupler to figure out transmitted power. Then you could adjust the oscillator coupling to balance the two.