3/4 vs 1" tree straps?

[Rain Man]

I've been using the straps for a few hangs, a couple of hours to a couple of days, and can detect no damage to the tree bark, but I am wondering if it is possible to cause damage that is not readily visible?

Absolutely. The damage is to the cambium layer under the bark. The bark is dead. Damage to the bark is more or less irrelevant. The tree can die weeks/months later, after the hammocker is long gone.