Backhand hitch type constructs are super useful for tying rope under tension to an object (and untying it under tension). The finishing two half hitches work well when tying, as the standing part tension can be maintained with the other hand when they are tightened.
The problem is that once tied, the two half hitches especially under little tension as afforded by the inner Munter-type wrap of the Backhand, have a little too much propensity for shaking themselves loose in my limited experience.
It is possible to replace the two half hitches with some more secure finish like Buntline or Gnat, but I don’t know how to tie, untie, and tighten them well while keeping the tension in the working part.
The last suggestion in the post - multiturn simple hitch - has some merit, but, as Roo would surely say, feels like throwing rope at the problem and I’m not sure if it’s any safer than two half hitches after Munter, Munter+ or Super Munter.
Sometimes throwing a little rope and some curvature at a problem can help reduce the tension enough to tie a slipped Buntline Hitch, as seen in the third diagram here:
Today, I was finishing a binding on a tripod construction with a single loop variant of the Versatackle, attached below, only I used smaller loop than what is depicted in the the attached diagram.