Hey OP
First off, I am not a headphone guy, but I do have Ls3/5A speakers for my reference system. So, at the last Audio Show, I got curious and listened to some headphones at the Show. Well, I was impressed. I always compare what I hear against my reference gear. I believe that some good implementation of Headphones could be very good sounding and satisfying overall.
The choices that perk my interest BASED on how it sounded and close to my main gear was presented by a Pathos headphone amps and T+A headphones. (forgot the model). Another one to consider is Felix amps and Audeze headphones. I do own a headphone gear (just the headphone) and it's an electrostatic HiFiman model but as I said, I'm not a headphone guy.
Ultimately, you need to go visit an audio show or a favorite audio store to check out before making the purchase. my post merely recommends brands that I heard that are close to the speed and tone of my Ls3/5a and ATC speakers.
just my 02cents