The center tap on NSTs are fixed and can't be bypassed or removed. I don't know how NSTs are "down under", but here in the US, they are potted in resin. They center tap them to keep the potential to ground lower. Think or your 15kv NST as two 7500V transformers sharing one primary with the connecting ends of the secondaries tied to ground. This way, there is a smaller chance of arcing to ground and the insulators can be smaller since each side is only seeing 7500V instead of 15KV. Just wanted to let you know. I don't want to see anyone fry their nice toys. NSTs are not so strong in that deparment. I have fried about 6 of them throughout my tesla coil history playing around with them.
BTW, you ladder looks great. Try using different metals, they have slightly different color characteristics when they arc!
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