Hip, hip, hooray for three mules
Or two or three strips of 3/4" mule tape in parallel. That's the stuff that is likely ideal, once it is cleaned of lubricant.
If I thought there was sufficient demand for Dyneema (tm) tree straps, I'd have commissioned them for production and resale. And, so, too would several other regular dealers before me who likely looked into it. <smile>
So, at a weight penalty of twice Dyneema's weight, mule tape, thin and optimized for tensile strength, may be the best thing.