While I like the HD800S (swapping between these and HD650) I find myself going to these specifically when I want more air, and closeness with sounds that are a little harder to discern through the HD650. The Classical music use makes perfect sense. From the Op list of musical genres, I would also think Jazz works well.
However, I would still not use HD800S for Rock and Blues, where I think a little more bass slam would help. I would probably lean towards Utopia, which is well beyond the price point - I know. But just throwing it out there as a my reference point.
I heard the Elear, and would definitely suggest a listen. It similarly opens up the sounds, in kind of an HD800S direction, but keeping with the bass impact of the HD650 - likely adding a little more. I did not listen on my own equipment, instead comparing the HD650 and Elear on the owner's equipment. They were within the ballpark. But I would have to recommend a listen first, if you can, on your equipment. If I were seriously considering the purchase, that's what I would have done. But I only found it slightly better than the HD650 during my brief listen. The owner did not find the Elear as musical as his HD650, and in the brief listen I could understand this.
The revamped EL8 open is my personal choice, a definite alternative to the HD650. I did not expect to like this as much as I did, after the fiasco with the original generation of EL8 closed. To my ears, the EL8 is not as precise as the HD650, which is hard to describe. The HD650 is darker, but quite precise in where it places instruments and how these sound. The EL8 is brighter (not bright!), just easier to hear the sounds. But then those sounds aren't as accurate. I usually just bring out EL8 when I'm tired of the other stuff, and I want to have a fun listen. You can also find the occasional crazy-good deals on the EL8. I paid $400 mid-year for mine.