That's because you're overpaying for an amp. I'd say HE-500 with a reasonably priced amp. (There are a few appropriate ones ~$250.) HD600 indeed cannot compete.
HD650 is closer and also darkish in the same way, but still behind.
None of the above match the timbre, which is really specific to 'stats.
(Just so you know, SE-5 slam is only comparable to orthos and perhaps some specific electrostats.)
Also forgot to mention - the pair was somewhat worn in the pads. Might've been a factor, but what I heard matches the measured signature.
Remember also that I said dark, not veiled. They are quite precise.