That isn't what I'm saying. You said you convert your iTunes purchases to .m4a before putting them on your phone. Which makes 100% no sense. This is like taking a 480p video and upscaling it to 4K on your display. It is STILL a 480p video. You are just creating a much larger file than needs to be [if the .m4a lossless file is much larger than the original iTunes .aac file, then you are wasting a lot of space].
I understand the need to convert, since there is nothing native on Android that will play .aac iTune files. But you might find a music player app for Android, that can - which would save a step in your process as well.

If not, you can just convert to a high bitrate .mp3 and it will take up less space than the .m4a files. [note: the .mp3 bitrate will need to be higher than the .aac bitrate to have the same quality - .mp3 isn't as efficient - 320kps should be more than enough, since I think iTunes is 192-256kps .aac]

Do a test. Take one of your .aac files from iTunes and convert a copy to .mp3 and a copy to .m4a Then look at the file size of the original .aac from itunes, the size of the .mp3, and the size of the .m4a. Then listen to each one and notice the sound quality between them 'should' be the same. Your sound quality can never be better than your lowest common denominator, in this case your original file.