I think that the best measurement you can make with a scope
is to sample the secondary base current with a wideband current
transformer.
The base current is a direct and rich diagnostic of almost the
whole system, and your instrumentation is well isolated.
Combine the secondary base current with a precise circuit model,
eg in Spice, to deduce the other waveforms with good accuracy,
at least in the region up to breakout.
Things get a bit more interesting and more difficult once the
system begins to be loaded by breakout. That's about the place
we got to with measuring and modeling about 20 years ago.
But start with the base current and a linear unloaded model.
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Paul Nicholson
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