Now I say this not knowing if anyone else has brought this up or come up with doing something similar, but I began doing this after having an extremely hard time producing progress with gearing my Pally after I was geared enough for heroics. When I started gearing my mage I didn't have many problems, mainly because I'm convinced melee, especially Strength Melee gear, was given the short end of the stick in Cata. I'm just convinced at this point.

In any case, when my Warrior was ready I decided to do it the hard way, sticking with regulars for a while until my gear was appropriate enough to be Heroic-presentable without inflating iLvl using pvp gear. Then, instead of just going to queue for randoms, I began to queue for Vortex and Throne of Tides, as I was realizing rather quickly on my other toons that these were, for me, far and away the easiest dungeons on Heroic...followed by Blackrock probably. I stopped caring about forcing the 70 Valor points. The result? PROGRESS! Just running Vortex and Tides alone gets my lower-geared 85s 490 JP per day. It's not the fastest route to buying pieces, but I queue for others afterwards and my attitude is that until my gear gets much better, however much more I get is all a nice bonus since some Heroics are just a total pain until you have more 346 gear and I have had just horrible luck in some dungeons seeing groups do well all the way through. Plus those dungeons really taught me very well on getting down interrupts and CC for more demanding Heroics environment. I knew how to do such things, obviously, but running the "easier" Heroics made me more prepared for the demand for them and it was good practice on how the Heroic boss drills tend to go for melee especially.

Stand here -> Move -> Interrupt -> Don't Stand There -> Follow Kiting and Interrupt More -> Burn Adds -> Return to Boss -> Profit

But I have definitely found that this helps with starting Heroics on the low end. I didn't know if anyone else had been trying a similar approach but there are definitely dungeons that are a perfectly fair challenge if you're geared in the 330 or so neighborhood and farm them until your gear improves. I really haven't been having any issues with Heroics now, it's just that for where your Gear is, some challenges are more fair than others.