I also recommend to observe the electrical-magnetical field inside and outside of these coil rather than the currents and voltages. I am sure you will be amazed with what you will observe and see the complexity. As these coils are not simple inductances, any parameter to change the interwinding capacitances as the tightness of the windings and enamel material and thickness the form material, isolation materials, coil leads lengths, placements of the coils on the bench, and other many other issues should be considered. The circuit and its requirements look like simple, but it is not definitevly a college class experiment. But unideal enviromnment can be thought as a advantage because generally things are discovered by accidents.
More uncontrolled conditions leads to more opportunity to surprizes.
May this forum offer a systematic wide spectrum analysis of this phenomenon. The thing that I observed while playing a kind of bifilar coil look like a RF electromagnetism anomaly. This observation made from different angles and from distance to the source and this behavior is always observed. Anyway any movement of the coil affect the waveform. This appears very much like a typical case of mixed magnetic and electric response.