Upgrades from HD650 are harder than they seem. I'd maybe try to get a listen to ZMF Eikon, see if they suit. Listen, not buy!
In your setup, I'd consider a DAC upgrade first. The 4490 DAC inside the Jotunheim isn't that great. I'd consider a better DAC, and a low-jitter SPDIF source to feed it (maybe homebrew Pi-based if you're trying to keep costs down).
Better headphones are going to be held back by your DAC. Hell, your current headphones will keep scaling with amps that cost ten times more, too. I'd consider these factors carefully before throwing money at it. Even the standard HD650 mods would give you a nice sonic upgrade for almost no cost, too.