I found a single Daily questgiver that will give me 275 aldor rep per turnin, but it looks like I'd need to do the daily 127 times to simply move from Hated to Unfriendly. Is this really the only way to change factions?
Yes, that quest is the only way to change factions. You're mistaking it, though; it's not a daily, it's a repeatable. So if you can grind / buy the items needed quickly it'll not take you as long as you think :)
If you weren't Human, it'll take you 1344 items, or 168 turn-ins.
With the level cap raised to lvl80, about the only reason to do this whole rep-grind is the "Hero of Shattrath" Feat of Strength, as the items the Aldor and Scryer faction provided - chiefly the shoulder enchants - are quite pointless at lvl80.
(Another reason you might want to do the grind would be if you needed an extra tabard to reach twenty-five; but there are a lot of tabards that are vastly easier to get, to the point that faction-switching is unnecessary.)
I hope you like farming because you're about to do a lot of it.
To switch from Scryer to Aldor, you'll need to turn in the quest More Venom Sacs roughly 168 times to get to Neutral with the Aldor, followed by a long Rep grind from Neutral to Exalted.
To go the other way (Aldor to Scryer), you can do the quest More Basilisk Eyes. Note these quests are repeatable, not daily, though both quest types share the same Blue Exclamation icon, Repeatable Reputation Quests can be turned in as many times as you like with no throttle.
You will get a nifty Feat of Strength for your trouble however.