I'll be interested in seeing how others respond to this. Most of my Tesla coil experience is in modern solid state versions. In my implementations, the primary coil resonance is negligible. It all comes down to the self resonance of the secondary. And this should have been determined long before this point in the build. Hopefully the self resonance of your secondary is at an acceptable frequency. I would use a signal generator and oscilloscope to figure out the secondary self resonant frequency and then match the primary to be close to that.
Once assembled, I have always tested mine driving the primary at a reduced voltage and using an oscilloscope with a pick up coil near the secondary. Sweep the driving frequency for peak output voltage. But that is tougher to do with a spark gap, but you could try using a hundred volts and see what happens (still using a scope with a pick up coil near the secondary). Max the secondary and try various adjustments to the primary.
-Jim