4K textures are supported in Starling and Adobe AIR they are just not recommended to be used. This is because only the latest mobile devices support 4K textures.
I can not select any of the PVRTC formats when exporting for ATF from the latest version of Texture Packer. So why I mentioned that it would be good to be able to do this. The only 2 options with PVRTC is the option which includes all the formats which is not ideal to use.
In regards to mipmapping this is correct you should export all mipmap options if mipmapping is required to be used, there will need to be a checkbox for this. I know as you say this will lead to blurry and overlapping images on lower level, it is a ridiculous requirement for mipmapping with ATF. If you don't do this then mipmapping will not work which is quite important.
For 2K textures you must export with at least 2 levels of mip mapping, which I think you are doing already.
Also the default quality option is normal for pvrtc but it still takes quite a long time to encode.