Just an FY!: I hung for years from untreated(but not in the ground) 2X4. The key was the top rail bar that spanned the 15 ft between the uprights and prevented any flex. Now, this was fence top rail in segments that was beefed up near the joints with a slightly larger diameter fence upright posts, with the top rail paced thru a few feet of the stouter fence post at any joints. As far as I could tell, it never flexed any amount that could be noticed. Probably could have also simply used another 2X4 - or even 2 of them if I was worried- for that top rail. But, I see that ascetics are important to you, so you probably will need something else. But, maybe not 6X6?
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