Texture Packer settings don't affect PNG output as far as I know, I just misunderstood your first post.
The setting you are looking for is this one
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However if you've already tried that and it still doesn't work it could be caused by another thing.
You say it is only happening on meshes. My guess is you don't have any white space around the edges of your image. The edge of a mesh will not be aliased. So what you want to do is add a little white space around your image.
Example:
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Here I have a blue texture and a green texture, if I export the blue one it won't have any whitespace padding and therefore there will be aliasing because it will be right at the borders of the mesh. If I export the green one it will be ok since there is a bit of whitespace.
With that in mind I think I'm actually gonna add in a whitespace padding option into the Photoshop export script 🙂
I hope that helps.