Hi Neil,
Back when I was a kid, I had a 24" machete that I'd rigged with a shoulder harness. One thing I learned was that drawing it over the right shoulder (if you're right handed), you can only draw the blade if it's as long as your arm or shorter.
Based on a clumsy experiment, I think you can draw something over your left shoulder that's a few inches longer than your arm. If I had to guess, that's why the soldiers are carrying on their off side. Someone with one of those daos may want to try the experiment and see.
Best,
F
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