What do you not like about the HD650?
If it doesn't sound as clear as it used to, replace the pads. The pads will only last about 1-2 years and when they get worn, you will lose about 5db worth of top end. New pads will sort you out, at least for a while.
Stock HD650 cables are a known weak point sadly, though they are usually good for at least a few years. I've had multiple sets of stock cables fail. Thankfully, they're cheap.
The Valhalla shouldn't be making static, either talk to Schiit themselves or try a new set of tubes. If there's static in one channel, swap the tubes from left channel to right and see if the static is now in the other channel. If tubes do nothing, send it off to Schiit to fix, they will. It should be a nice amp for the 650 when it's working.
IMO there is not much under $1k - or at any price - that's a straight upgrade from the 650. But there are some headphones that are vaguely similar while being better at certain aspects.
You can now get a Focal Elex from headphones.com with warranty. The Elex is a very nice headphone, brighter and a bit sharper but with a fairly similar tuning, very good punch and impact, lively dynamics, and good instrument separation. It's a more exciting listen, but also less natural and a bit more metallic sounding. I like it, though I consider it a sidegrade. For $400 it's not a bad deal as long as you buy it from headphones.com since these headphones are known to be fragile, and you'll want the warranty. They're also very pretty but a bit heavy.
You can try a Stax L300 or some other similar used Lambda. You'll need an electrostatic amp to drive it. This will give you the best clarity you can possibly get your hands on, but estats are a completely different barrel of fish and come with their own quirks that you'll have to live with. However, if you want an actual upgrade on the HD650 in terms of resolution, this is one. With a bit of tweaking, and probably some EQ, these will give you world-class sound quality, but might need some setting up out of the box.