Your Linn Unidisc should be a pretty good source. I would hold onto that and get a decent amp. I've heard the Schiit Lyr but not the Woo audio. As for the headphones, try as many as you can before you decide. I thought I was going to end up with LCD-2's but found that I liked the 702 anniversaries more after a few trials.
Also keep in mind that the HE-6 is more power hungry than the other 2 you mentioned.
Pre order a fully upgraded geek pulse. Includes fully balanced dac and headamp, femto clock, linear power supply and an audiophile usb cable. Decodes DSD natively- unheard of for the crowdfunded price. Last chance to get one on the followup indiegogo campaign.
Can you get any of those 3 phones on approval? I love my HD800'S but don't have your portable front end. I play mine mainly through either DX100 C4 or AK100 and have no complaints. The HE6 has a phenomenal reputation for good sound too. I have not had the pleasure of listening to it.
I will also say it will take many hours of listening to truly appreciate what you do finally end up with and you have narrowed your choice to 3 very good phones. Do you listen at high volumes and what do you listen to mainly rock, classical, jazz? I am a rock fan but I have a collection ranging through acoustic folk 60s synth pop heavy metal classical AOR anything goes. I have no need to reach for another phone whatever comes on and whatever mood I'm in.
The word of warning I would give about buying the HE500 without audition and not on approval is you will always wonder what the other 2 options sounded like and upgradeitis will eventually scratch away at your soul....
Email moon audio and see whether they can offer the 2 top ones for you to try. Then try both the HE6 and HD800's. Can these 2 justify a $700 difference? No.
But are they endgame? My thread says yes. I'm thinking if you're considering spending $1600 the HE500 may not be endgame.
One more thing; have you considered buying either phone through the classifieds on this forum? You will get much better value for money that way and the headphones will still be the same
I've not tried the SR71B with the HD800's so hence I said see how you go. I'm sure the combo will be great. You've nothing to lose by trying it. How far up is your volume for running your pfe232s?
I wouldn't get rid of them either I'm sure they'll be a good complement to your over ears in situations when you want to listen to music without sound leakage.