Ok, let me tell you about my own experiences in this matter, as a dedicated Paragon player since Nightfall's release.
One easy, yet effective solo farming build I've found to work in many situations is simply a P/Rt spirit spammer. Bloodsong, Vampirism, Signet of Spirits, etc. along with Spiritleech Aura, Armor of Unfeeling, and/or other spirit enhancing skills and Spirit Siphon to manage energy works for farming whatever Nicholas might be collecting many weeks.
I long ago tossed out my starter armor, so I haven't really done much testing with 600ing, but that might prove harder on a Paragon, with high armor ratings to contend with, in addition to the slower energy regeneration. 55 hp builds are "workable," though. I have found that taking a Bonder hero or two works out best in that situation. If you plan it correctly, you can even get by with 2 copies of Protective Bond placed on you from 2 monks, without fear of them losing energy (they split the cost) or having to constantly recast Protective Spirit.
Sadly, in these cases, as well as other farming builds I have come up with, my Paragon has not really the ideal profession for such feats, as others have said a few times already. She ends up forgoing many of her own class skills in favor of becoming a "wannabe" version of another class. There is a P/Mo Dead Sword Farm build on PvXwiki which does use mostly Paragon skills, but I find it to be too much trouble to juggle all the echos and whatnot for my taste. The build I keep falling back on when I want to farm mindlessly is that spirit spammer I mentioned.
As far as elite missions go, most of the time it boils down to playing an Imbagon if a group will accept you at all. In a few team builds of yore, I've seen "Porogons" (P/Rt with Vocal was Sogolon and some party-wide shouts, like Fall Back! and There's Nothing to Fear!) being of core importance, but alas, I've personally yet to run into anyone who has asked for such in outposts.
Keep your fingers crossed for some Paragon loving in the upcoming skill balance! In the meanwhile, I'll keep trying out crazy ideas and tell you if I stumble across anything outstanding.
