Honestly I think people overstate the need for huge resistances. A lot of people have been going out and stacking as much resist/vitality as they can and largely ignoring damage stats and have been having little success - this is no surprise. In order to efficiently kill champion packs you want to keep your damage as high as possible. As a bonus, dexterity directly translates into dodge, armor and damage for Monks, making it easily the best stat to stack.
I have cleared all of Act 3 now on inferno (both solo and duo) and have to say that just getting more damage helps tremendously and armor helps tremendously. The ordinary white mobs are scarcely a problem (with a few exceptions of hard hitting ranged mobs, although most projectiles are avoidable) and champion packs require some sort of kiting when attempting the content without over-gearing it.
I currently use the following build and here is a screenshot of my stats:http://us.battle.net/d3/en/calculator/monk#WTXYgk!YcX!acbcYa
As an aside, I would suggest getting a lot of dex/armor instead of resistance at first, and then adding resistance later on (I did this, and completed Act 2 and most of Act 3 with less than 200 resistance to everything). The primary reason I suggest this is that Armor and Resistance do exactly the same thing (because armor mitigates all damage), and when buying gear from the AH, items with +armor on them are almost always bucketloads cheaper than items with all resistance.
People will likely question some of my build choices (for example, crippling wave over Fists of Thunder or Deadly Reach) so I'll briefly explain some.
Crippling Wave - This has an INSANE amount of aoe damage output, because Mangle takes the damage to 143% weapon damage, which puts it only 2% weapon damage behind runed Fists of Thunder. However, it has significantly better aoe damage than fists of thunder (which only does area of effect damage every 3rd attack, and even then, only in front of you). I'd encourage more people to try crippling wave as their primary source of damage (If you're trying to progress on a particular fight, for example, butcher, obv. you want FoT because it is higher single target dps because of the faster attack speed).
Mantra of Conviction - This is basically my spirit dump. 48% more damage while spamming it every 3 seconds is an incredible amount and you'll really notice the damage difference combined with the additional damage from the runed Breath of Heaven and Blinding Flash. Against champion packs, most of your damage will come from rotations of serenity/blind/seven-sided strike, before kiting briefly and repeating it. When I play with multiple players, I will sometimes switch to Evasion with the armor rune because everything hits harder (in my opinion, melee gets progressively worse the more people there are in a group)
Breath of Heaven/Serenity/Seven-Sided Strike/Blinding Flash are all pretty self explanatory, they're all defensive abilities which provide amazing offensive utility as well.
The final one people will likely question is Chant of Resonance. This is a great ability for champion pack killing because of the spirit regen it provides, so many times when you're kiting and out of defensive cooldowns you'll run out of spirit and won't be able to safely re-engage without just praying for an initial dodge to get the spirit for serenity/blind. With this passive, you won't need to. I also use a helm with ~1.5 spirit regen/second which I find helps out tremendously. I obviously swap this out if I'm doing a boss that I can't farm with 5 stacks of Neph. Valor. (I will likely get rid of this passive and take either the cooldown reduction one, or the 8% damage one if and when I finally get an awesome weapon that also has spirit regen on it - about 3/second total is enough to allow kiting while regening sufficiently).
If you have any questions, feel free to ask away.
EDIT: I sometimes use Deadly Reach with Keen Eye for specific bosses or when grouped; 50% additional armor is huge. Obviously enchantress is the best companion for soloing as well (15% armor/3% attack speed is a lot)