Dang. That swatch of carbonization looks like it involved a half dozen turns or more. That could sure play hobb with the 'Q' factor as well as alter the inductance.
Re. the sweep test, what you'd wanta do is leave coil and cap in parallel, with the lower end grounded. Then connect both genny and scope to the top (with their cable shields grounded, of course).
A parallel-resonant LC tank (which this is) exhibits highest impedance at resonance, grounding out all other frequencies.
But a series-resonant tank (L and C in series) exhibits lowest impedance at resonance, making it useful as a wave trap to ground out an unwanted signal.