Hmmm, in the past three days I have almost tripped over parchments while loking for other things. Hopefully you don't mean 3am east coast, that is still a major west coast time...and 2-3 am west coast last night, just after restart, I saw one other person on in two hours of play.
Parchment spawns: Pyrimid: Middle of 'streets; where the foes walk. In the end 'rounds' There are two spawn sites in Palace of fire behind the initial foe.
Sphinx: Near the Beetle in entrance hall (other side of platform) Hall of Champs and Arena: Same as pyrimid, streets and end rounds.
Just make sure you are being honest with yourself and going at a real dead time. If all realms, including Ambrose, say 'Perfect', go for it. I have picked up many this way.
Note: They sell for a very good price, so many pick them up to sell, so check Bazzar.
Do vault of ice instance, and just reset the instance after you cleaned it out. I can't say it's fast, but hey it will get you parchements without competition.
Oh side note if you think getting parchements is bad, just imaging needed 80 scrap irons for your marleybone crafting, oh and other items too, and don't forget the 9 hour cooldown on 5 items and 8 1/2 hour cooldown on the other 5 items.