The AKG K371/K361 are the current gold standards for closed-back accurate studio headphones and I imagine they will be for quite some time, so I think you made a great choice. I’m sorry you’re having to wait for them. They had some availability issues due to their popularity, and the current virus situation has exacerbated that a little further. When this is all over and I get back into the tech reviews groove on a more normal pace, I can’t wait to get my hands on the Bluetooth versions.
The 599 SE is *really* close to the 600-series, to the point where I agree the 600’s may not impress as much retroactively. Did you end up enjoying the 6XX’s?
If you end up trying and liking a Grado or a Beyer, you’ll know you’re a “Treble/detail head” and you can work forward from there.