Hey - water test is a great one! Just like soap water test for tire pressure. Good one.
In hind sight - this is a case and point on faulty decision making and faulty analysis.
My error became so clear after a good night sleep:
1. I was prejudiced that the easy failure of the part was because some crazy cost cutting scheme in how this part was made. I was convinced that the "core" was probably some magnetic/ferrite-power painted on layer that easily melted... I was seeking confirmation for something I already subconsciously decided: must be some cheap core, cheap coating... whatever. Such bias impeded me from really carefully thinking about the problem.
2. My test of the wire was faulty. I held down the DMM probe lightly. I was concerned that the probe would just scrape off the insulation coating. Pre and Post unwind resistance may be more telling. Continuous measurement of the resistance as I unwind the wire might have been even a better way. At the time any "short" is unwind, the shorted points are no longer touching, there would have been a jump in resistance. It might have been easier to notice on the DMM when the reading jumps.
This may not have worked - the wire may need the current (heat) to expand to force the small "holes" to touch. A better way then DMM to test burn-through insulation was needed.
3. I was 2 dimensional instead of 3. I got locked in thinking if there is a short, I have 61 out of 62 loops. The short doesn't have to be adjacent loops. It could be from one layer to the next. The size of the core allows 3 loops side-by-side then the loops must go on top to the next layer.
For example: a short between layer-1-bottom-loop doesn't have to be only with layer-1-middle-loop. The short could be from layer-1-bottom to layer-2-bottom loop thereby taking out 6 loops (wire could go layer 1 bottom, middle, top then layer 2 top, middle, bottom.) So one short doesn't take 1/62 out, it could take many more.
So, my thought about 1 or 2 shorted turns should not matter is silly. It was 2D thinking and the coil is 3D.
Reaffirming the need for better decision making is always a good thing...