I do much the same, including a separate player and trying iTunes substitute programs.
I did not know you can't save the iTunes songs to another place on a Mac.
I can't on my iPad. I don't have a Mac desktop or laptop anymore. I'm not sure if you can move them on a Mac computer or not.
My last Mac died, and I haven't needed to replace it. I like the standardization and availability of apps for Windows better. It's not necessarily better or worse, just easier for my brain than the Mac OS.
I bought file managers for my iPad, and their function is extremely limited. I can't move pictures or music. The OS determines where to put them. Apple wants to be the boss, and I figure it's my computer, I should be the boss

I'm not a streaming person, I like to own what I like and when I buy downloads, I also store them on either CD or Flash media so if my HD crashes, I don't lose my music.
Insights and incites by Notes