I prefer to listen to recorded media via ...

I use hearing aids, too. But not the inductive loops (uses the telecoil, right? lots of EM noise, right?)

My method is Direct Audio Input to jacks on the back of my hearing aids. My preferred setup is a pair of modified bluetooth headphones with short wires leading from audio jacks (my addition) to my hearing aids. I can then listen to music with background sound too, or turn off the hearing aid microphones and hear just music.

I voted the first option.