I have aphantasia, and I also remember songs in multiple parts vividly. I won't go so far as to say it's eichoic--I can't, for example, turn around and just play a version of it on piano like some people I know, and I'm fairly sure I'm recalling an approximation in a lot of cases--but it's a detailed enough recollection I can "listen" to songs that way by recalling them. It's very much in contrast to my non-existent ability to recall even a familiar image.

I've considered cause/effect on this before and personally just decided it was probably coincidence combined with my poor visual memory making the other types seem that much more impressive. There's no particular compensatory mechanism I can think of that would explain remembering sound better because I remember vision worse.

Interestingly, I've never been any better at composition (i.e., imagining novel music) because of this. To the extent I've composed, I still pick stuff out a part at a time and figure out how it fits rather than starting with a finished sound in my head to recreate.