High tension carbon strings would be best for the trebles as these will give you much more tension. I prefer a normal tension High E though.
The only problem is that they tension can be high enough that the strings will slip through their own knots. If you have a slotted bridge you could probably make a super knot that doesn't slip, worth a try anyway.
I'm not sure how many times you'll need to wrap the strings around those steel-string tuners though.
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