Need to wait until they arrive (this is going to take several weeks actually). The price is the same as usual (995 USD I guess) but I was successful in getting them absolutely new, unpacked for 880 including shipping and fees (US). Now I need to get them from States but have a plan already.
In my opinion, if you are after perfect neutrality (i.e. you want to hear the source, not the gear), O2 + ODAC + headphones like Audeze LCD-2 (or Hifiman HE-500) are going to work absolutely fantastic, based on objective measurements from sources like Innerfidelity or headphone.com. When I'll finally receive LCD-2, I am not interesting in any other upgrades related to the hardware part of my audio chain for several years at least. You absolutely don't need anything like tube amps etc. if you are after fidelity (as close to source as possible) and not distortion (even though it can be pleasing as you can see with vinyl or already mentioned tube amps). You already have objectively fantastic amp and DAC so you should get a very nice pair of headphones to get the best out of your multimedia.
As for Stax or LCD-3, they must be stunning but honestly, they are definitely not worth the money... If you try to properly EQ your HD598 and then compare with some high-end, you are most probably going to realise that the difference between 50 dollars and 5000 dollars is definitely not DRAMATICALLY high. Just my opinion...
To finish up, I am really glad you decided to purchase O2+ODAC... Absolutely worth every dollar.
Will give you my opinion on LCD-2 as well later :-)