Step 1) Make a new, free Account. There's a link in the log-in popup, just above where you enter your Account Name*. All you need is an e-mail diff from the one you used for your current account.
(* I recommend that your new Account Name be a spin off your current account name, and then that you use the same password, or something just a letter or three off (for ease of remembering), but whatever works for you.)
Step 2) Make an "Opener" character on that new F2P account. Literally any build will work for the "opening" function, but you'll want to consider which alt will actually be "running" the quest, this one or the new Favor Farmer from your main account (read below). If you're in a hurry I'd use something like the Barb DP runner (link below), but there are other thoughts:
(You'll have three character slots in a new F2P account - up to you what to do w/ the other two. The "Dual Box Openers" in the 2nd link above are for leveling newly reincarnated alts, dragging even weak starting builds through any Level-appropriate content - not a bad dual-purpose concept. You can also make a "main" for that account, a
solid, working F2P build that can level and earn DP (to buy the opener account new content to open). And/or multiple openers at diff levels for future alts on your main account. All can become mules as well as openers, or whatever. Or just ignore the other slots - lots of ways to roll.)
Step 3) Learn how to Dual Box.
http://ddowiki.com/page/Dualbox It's legal in DDO, and done a lot, and for a variety of reasons. Handy skill for any account.
Step 4) Using your current experienced alts as openers for the new Free account, dual-box a group that includes your new F2P Opener, and level them up to whatever level you want. (Level 1 can be used to open anything up to a Level 3 quest*). Run them thru each quest you want on (at least) Hard, so they can now open Elite.
Step 5) Favor Farm! Now you can group any new alt on your main-account, who will be your "Favor Runner/Farmer", with your dual-box opener, and your new alt can open Elite on any/all quests**. Knock out some of Korthos* and the fast Harbor quests for 100 Favor, knock most of them out for 200. If you fail, just heal and (quickly) re-enter - experience doesn't matter if all you're after is favor, just complete the quest on Elite any way you can.
(* Your new alt will emerge on
"Snowy Side" Korthos. Your Opener will end up on Sunny Side, so your Runner will need to leave Korthos to the Harbor before joining the Opener's group. No big deal, no changes in the quests, just has to happen. (Thks K!))
It's up to you whether the main account FF'er is the one running the quest and the opener just sits somewhere*, or whether you follow the opener around with a drone from your Main account while the opener crushes the quest (slower, but not all have Vet I status to create a new Lvl 4 alt).
(* I like the Hall of Heroes, near the bank/auctioneer/teleporter/guild ship/mailbox area. To keep the Opener from disconnecting, hit [Escape], and click [Log Out] - but don NOT "confirm"! Just let it sit there (you can drag it off to the side) and that alt will never Time Out. Note that this may only work the first time you try this trick it on any log-in, the next time you may be logged out (depending).)
If your main alt is actually running the quests, just use the strongest/fastest build you can. If you only have F2P classes, I like a Human Str-based Barbarian w/ DM of Passage for running speed right out of the gate (some variation on the "DP runner", above).
Just make sure the Opener 1) has run the quest on Hard (or better), 2) has the quest (you can "share"), and 3) has turned it in for reward (so it's not "pending"), and then it doesn't have to accompany the Favor Runner. A good build should be ample to crush 100-200 Favor worth of starter-Level content in Korthos/Harbor/etc. in a couple hours, done, delete*, repeat.
(* In my experience, the best Favor Runner builds will start to fail around Level 5-8. They're just too front-loaded, built to crush early content and run fast - but once they've done their job, who cares about "later"?)