Maya "Convert to File Texture" and "Transfer Maps" are still limited to small 4k.
It should be possible to bake at least 8k maps.
Especially Convert to File Texture from a Maya Shader network is nothing you could do in another application outside!
And about Transfer Maps see also at the old idea request:
https://forums.autodesk.com/t5/maya-ideas/better-texture-baking/idi-p/7957419