Very tight hitch around circular object - best load distribution

Is it ? We have to measure it. The midde of the three segments of the 3-wrap side is / remains possibly more tensioned than the others, so I believe that the total “push” to the surface of the pipe from the two sides will be almost equal.

Yes. Read in the relevant threads and posts what is written about the danger the hitch “closes” prematurely.
The trick is to first tighten each “half” of the hitch somewhat, pulling each end against the pole, but not towards each other, so they will not be transported towards the middle of their distance too early - and only then, when the hitch is already somewhat tight, and most of the slack is consumed, to start pulling them so the bights connected to them start to approach each other.
Also, do not forget, at the end, to pull the ends one by one, the one after the other, alternately, as we have to do with all tight hitches.