Your distorted recording has the amplifier clipping like crazy. All amplifiers clip when they are trying to produce more output level than is possible. You need an auto level control or compressor circuit but some circuits react too slowly then the distortion comes before they cut the level down. Maybe you have the mic touching and moving on the chest.
When I tested my electronic stethoscope I mounted the mic on a peanut butter jar plastic lid then the lid touched the chest and blocked background noise and the mic was not touching the chest. I was able to use an LM386 power amplifier and loudspeaker without having any acoustical feedback howling. My heart sounds were loud and the amplifier was not clipping.
Bose provides no spec's on their expensive headphones like frequency response, maximum power and impedance. They just say important things like the PRICE, color and weight.