I listen to my main system at 65 - 70 db typically. Sometimes crank a bit to have peaks get around 80. It is the expansiveness and wide deep soundstage that is so compelling although I can feel it.
I have pursued a great headphone system for at least fifty years. I have developed stationary home and office systems and traveled with portable DACs, head amps, of all kinds. I stacked up tubed equipment in my office... I have at least six sets of top of the line headphones. They always sounded like they were in a different class of experience. Sort of like a great sounding transistor radio. But as you describe.
Then I bought the Woo WA5 headphone amp. It has so much power you can connect speakers to it, huge current. I have a set of Takayuki 300B tubes in it. That is a completely different experience. The full midrange - bass and power behind the sound is completely different then every headphone system I have ever owned or experienced. It is incredibly compelling and addictive. It is hard to put down... like my main system. It fills the void I think you are describing that headphone systems are missing. Maybe it really is the sound hitting your chest... but maybe you are missing what I was.
You can see my main and headphone system under my user ID in virtual systems.