Yeah they don't tile horizontally because this height map is part of 4 different height maps so unfortunately I can't make it tileable in that direction.
Thanks for the advice, however I'm not too good with Pixel Processor, and don't even know how to sample those near-the-edge pixels and copy them in needed directions as you're suggesting. Is it possible to do it with some node(s) involved?
An alternative :
I notice your map is 2048 x 2048
So what you could try is :
Add a transform 2D node set to absolute at twice the resolution i.e. 4096 x 4096. Set the transform to /2 and offset to X 0.5 and Y -0.5 . That puts the original image in the lower left quarter
Follow that by a mirror greyscale X axis 0.5 This makes the new larger image tile horizontally (it already tiles vertically)
Then HBAO
Then a transform node set to absolute 2048 x 2048 (same as original image) and offset x -0.25 Y 0.25 that takes the output image from the lower left quarter

Dave