The left part is how it appears in CC3+. I have successfully exported other images at 6000x6000 with no issues. I should mention, I have looked at all the different layers and sheets just to make sure this wasn't a "feature" of the map.
As well, when I exported it at 2000x2000 - no issue.
Does it export at sizes like 2100 (the next power of 2 above the working size) or 3999 (just below the nice round number)? Also, are you using antialiasing in the export?
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As well, when I exported it at 2000x2000 - no issue.