Yes I built a similar oscillator, a bit cruder though
I clipped my scope probe to the output and connected the
probe to the counter. I noticed that the frequency drifts somewhat
when the crystal is first plugged into the test oscillator.

Highly recommended reading;

"High-Performance crystal filter design" by Bill Carver, Communications
Quarterly, Winter 1993.

Addresses the same problem and lots more, and unless you plan on permanently
attaching your fingers to your filter, you'd better pay attention.

W4ZCB