The K550 was a disappointment imho - having been a big K701 fan and being at least familiar with some of the older AKG studio designs. They aren't terrible headphones, and compared to more contemporary ~$300 closed headphones (the ones that don't completely suck - so let's say, the AT A900X, Klipsch M40, Sony X10, that kind of thing) they stand up relatively well assuming you can get a good seal. Personally I like the B&W P5 and ATH ESW9A better at the same price point, and the Kenwood K1000 better at a higher price point. Basically I found the K550 to be kind of flat sounding, with a bit of upper-mid emphasis; I agree with you that they aren't harsh, clashy, or sibilant, but they just didn't do anything for me beyond that. The ESW9 have better mids and more textured bass, the P5 have more isolation and overall texture, and the K1000 (which I have not A/B'd to the K550 - the other two I have) will likely best them when it comes to soundstaging and overall extension, and certainly have a (to me) more enjoyable mids oriented presentation.
Having said that, if you're raving about the K550 over basically everything you've ever heard, they're probably a good match for you. My complaints based on the above are more related to preference than any specific gripe with the K550 (they're well built, they sound fine, nothing really sticks out and says "wow this sucks, don't buy this!"). And based on that, I'd probably just go ahead and order them and enjoy yourself.
Regarding the AH-D600 specifically, I cannot say I've heard them - I can say that I've seen A LOT of mixed feelings about them, some people really seem to enjoy them, and some people really seem to despise them. They certainly have not filled the AH-D2000's reputation (and honestly I didn't think the AH-D2000 was the best thing since sliced bread; the K550 for less money is probably a better choice there - build quality feels MUCH better too). Additionally, my understanding (and this seems to be one thing various people can agree on) is that the D600 is a relatively bass heavy headphone. I know the D2000 before it was. I wouldn't consider that kind of sound signature if you like (or love) what the K550 are doing for you. But take this with a massive grain of salt, given that again, I have not tried the D600.