Your tickler coil in this case could be called a "loose coupler" (old radio jargon) and will work just fine as a drive for the 2N3055 as long as long as you don't significantly increase collector current.
What is so puzzling about how the circuit operates is that once oscillation is initiated, the "tickler coil" seems unnecessary insofar as feedback is concerned. Sweeping a magnet past the tickler is sufficient to initiate transistor turn-on and startup the oscillation, but one must wonder what the actual feedback mechanism is which sustains the oscillation. Is it internal to the transistor such as the Collector/Base capacitance or is it something else? Perhaps TinMan will substitute a small signal transistor such as the 2N2222 in place of the 3055 to make comparisons.
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