Stuck in the middle (Gearscore)

So I've gotten a few characters now to max level and I end up with the same problem on all of them and I usually start leveling a new character out of boredom. I reach a gearscore of around 4.8k and can't buy any better gear on my characters from the emblem vendors, other then frost. I don't have the gold to buy any gear on auction house. So the problem is that nobody is willing to take any of my character to any raids other then VoA with that gearscore. It's usually required around 5.5k for any raid at the moment and I have no idea where to get the remaning ~700 gearscore from.

Am I missing something I should be doing to get that last GS to start raiding?

Are you full 245/232s? You can obtain this via heroic ICC dungeons and emblem gear. Also, prices are inflated now but there are cheap 264s available on the AH, maybe farm gold right after squish and get some. You should be able to reach at least 5k GS without touching a raid, though. If anything keep farming VoAs for gear as well. Get in a group to do the weekly Must Die! Quest. Do your daily HC every day for EoF. Lots of things to do

Well my paladin for example is currently 4715 with only 4 items below 232 and they are trinket, ring & bracer which is a very low gear score upgrade if I were to upgrade them. It wont bring me close to 5k. But the problem is still getting to that golden number of 5.5k that everyone is asking for to start raiding. Even if I were to get 5k without raiding, nobody would take me since I am missing 500 gearscore and without any achivement.

Join a guild that runs ICC 10man raids, and ask people to inspect you and explain them that by upgrading gear score you are not actually upgrading your dps or healing or w/e is that you do. All it takes after that is 2 or 3 lucky loots and some more frost emblems so you can work on your tier 10 set. Avoid pugs unless you are near BiS and you want to join groups with 6k requirements.

If for any reason you can't join a scheduled raid so finding a guild is not option, raise your cooking, fish at WG for fish feast materials, cook them and sell stacks of them ( after the gold squish though). Then you can buy some BoEs. Boots are always a dope upgrade so I aim for them on my fresh 80s.
Also the points shop has some nasty pieces!