I disagree with KISS. For a properly-tuned SGTC you do NOT need a breakout point, and in fact that may cause its own problems. It could reduce your overall arc length because it causes corona leakage and does not allow enough voltage to build up to form a proper streamer.
As for your popping fuses, what are you using as a ballast for your MOTs?
Regarding the spark gap not firing, there are a few things that could cause this. The first is that as the electrodes heat up, their properties change and they may become less conductive, and they may start to shift. Steel is generally not preferable for this type of application as it is a poor conductor at high frequencies and the melting point is relatively low. Tungsten is much better for use in spark gaps, though I understand it is harder to come by and more expensive. The other problem is that two MOTs will only give you about 4-6kV, which is very much on the low end for a Tesla coil. While it is definitely still doable, the spark gap must be finely tuned and cannot shift at all during use. You mention vibration, which could very well be the main cause of this issue. Additionally, I suspect your spark gap is asynchronous (not timed to match the charge/discharge cycle of the tank capacitor) and that will affect performance. If timing isn't right, the capacitor charge/discharge cycle will be disrupted and your spark gap may not fire reliably.