Unless you're listening quite loud, I've not really heard of people having issues with open backed headphones and using the ModMic. Sound leakage could happen, but it's unlikely to bleed through to your mic unless you have it very loud, or if it does it should be pretty faint.
The HD 6XX drop just ended, so it's likely to be a few months before it drops again. Do you have a preferred sound signature or genre of music you'll be listening to when not gaming? Do you really like instrumentation of songs, the vocals, the sweet thumpy mid-bass, that deep rumble of electronic sub-bass, and have a preference over what shines just a little more over the rest?
The DT 990 is a good headphone, bright in the treble, slightly V-shaped, decent mid-bass boost, but starts to roll off into the sub-bass just a little. It would be a decent choice if that's what you want. If you want something with a bit more thump in the bass to it, the Fidelio X2 Azamonde suggested is good. If you want something with a similar sound signature to the HD 6XX, the HD 500 series will have the same... type of sound, if perhaps not the clarity, and they will all sound just a little different. The 598 is a popular pick. You may be able to find some used HD 600s or [or even HD 650s] around that price range which will be a little more neutral than the 650, slightly less of a bass boost, and little brighter treble. Or alternatively buy a 6XX off someone on /r/AVexchange. I've seen them pass by there for around 180-200 shipped sometimes. The AKG-7XX off massdrop is definitely an option if you've got a Schiit stack, it's not as popular as many others but still a good set of cans if you have the power to run them properly, the 62Ohm resistance misleads many people about the difficulty to drive those properly.
And if you want to stick with closed backs, the DT 770s are a well liked closed back, although some find the treble a little sharp or the mids a bit lacking because of the "V-shape" of boosted bass and treble with recessed mids. Many people like the ATH-M40x and M50x, some like one over the other, hard to suggest which one.