This assumes you have ONE open slot or a character you don't mind deleting or can buy one.
With one slot open, create a character (don't do DC because you get stuck in that Cold Harbor quest and can't port out ... if you do it's only a few steps)
Spend 0 time on character, take all random.
On entry, port to players in your guilds. If you see a port to AlIk'r Desert grab that one.
You will hit level 2 in about 4 ports. I could get to level 4 in less than 10 minutes just porting around. You can also port to your different houses, outside of house run out and grab points there too.
Hopefully you get to Alik'r Desert and join one of the groups. Port to group members. After 3 anchors you are level 5. If not just do another anchor.
At level 5, you have gained 4 levels. Delete toon creat another one and do the same. Now you have 8 levels. You can delete 3 toons and will gain back one every day. In a fresh slot, you can do this 4 times on new characters. That gives 16 levels gained. Wait one day and do this again and you have 20 levels. Lazier players can only go to level 4 ... in less than 10 minutes just porting around.
You can buy a character lot and you will get to do 4 lvl 4's the first day. IF you have to delete one, you only get 2 deletes the first day. And then it resets 1 each day. At any rate, this is way way faster than leveling the same character, even to level 10.