For me, no question the best headphones you can get with a $1k budget is a second-hand pair of Sennheiser HD 800, and occasionally 800s if you find a good sale. I think I'm going to try Focal Clears next though and they have potential to be a contender too.
If you're talking MSRP, I unfortunately can't help with that since I don't buy headphones at MSRP much anymore. Maybe one of the ZMFs in this price range but I can't even remember if they are actually around $1k or slightly higher. Atticus for instance.
For what it's worth I think you hit summit-fi sooner in IEMs than headphones. At $730, the Thieaudio Monarch is I'd say summit-fi tier, now granted not the top of summit-fi but still in that ballpark. At $700 in headphone world, you have the Ananda which, don't get me wrong I love the Ananda and it is amazing, but I think you are still a ways off from summit-fi.
I'm not sure if I'd even say the HD 800/s is summit-fi at this point, I love them a lot but especially after having heard the Stax 009 a few times, there is still a ways to go from the 800 in many key areas. Let alone stuff like the HE1000se which is just godly on like every level, and then Susvara beyond that.
EDIT: To be clear the 800 is still remarkably good though. Probably my favorite headphones all things considered, even including TOTLers I've either heard or owned like the ones mentioned above. EQ helps a lot to address some of its biggest issues tonally and I'd say it is actually summit-fi on the technical side of things.