Modern Ignition issues

I am also running a shorai battery and would doubt it had a short, I had thought you had a regular battery so maybe the battery is ok but just to take it out of the equation I would try a different battery. I really think you need to run a ground to the head from the battery, as motorson stated "good grounding is critical"
The harmonics of the engine at 4500 rpm may be causing temporary ground contact. Looking again at the scope image the peak voltages on the secondary side are quite uneven.

Hoping you get it sorted
Craig

Assuming carbs are balanced and timing good it does sound like harmonics and a damaged wire/connector. Earth has been suggested but the cable from the timing cover also does this as it ages and breaks down where it exits the case and corners up to the frame.

So any news?

Craig