Nicholas -
A few areas of concern are revealed by your photos:
1. It looks like your tank wiring to the MMC and spark gap is
extremely small gage stranded wire (#16 AWG?). All the interconnects
between primary coil, spark gap, and tank capacitor need to be fairly
heavy gage (I recommend no smaller than #12 AWG for a small NST
powered coil). The peak current in the tank circuit can be hundreds
of amps when the spark gap fires and the tank capacitor dumps all of
its energy, and #16 AWG is not adequate.
2. All the wiring in the tank circuit needs to as short and direct as
possible. You didn't post any photos of the overall coil and all the
interconnects, but I suspect that your primary wiring may be longer
than necessary. It appears that you have carefully calculated the
inductance and resonant frequency of both primary and secondary
coils, but I bet you did NOT include the length of the additional
tank circuit wiring in your primary coil calculations. Measure the
total length of your primary wiring, include this in the length of
the primary coil, and re-calculate primary inductance and resonant
frequency. It may be much lower than you thought. You may need to
relocate the spark gap and the MMC to keep the primary wiring as
short and direct as possible.