I would have thought that you would reduce the effect of the jitter by filtering the correction signal that you are using to discipline the other oscillator.
I was involved in the design of
this GPS disciplined oscillator, where there was quite a lot of digital filtering of the correction signal. As the oscillator being controlled was itself a good ovened oscillator, there was no need for wide ranging corrections. I don't know what type of oscillator you are trying to control, and you might need faster or wider ranging corrections.
There is also a problem with using a 1 Hz resonant circuit. It won't free-run at the correct frequency. If you are exciting a resonant circuit at 1 Hz, it will oscillate at 1 Hz, and the amplitude will depend on the Q of the circuit and its self-resonant frequency. When you cease exciting the circuit, it will oscillate at its self-resonant frequency, and the amplitude will decay at a rate dependent on the Q of the circuit. The frequency during free running will not depend on the previous excitation frequency; it is only the initial phase that was controlled by the excitation frequency.
You could make the 1 Hz oscillator part of a PLL, so you control its frequency, and then it would run at the correct frequency during free-running. However, it would be a lot easier to use a much higher frequency oscillator and a divider in the PLL, which then becomes the GPS discipled oscillator you were making in the first place.