Probably one of the best ways to rapidly gain levels during this gap is through the Abandoned Sewer Network trial. To get this trial, go into Founders Falls and visit the contact near the Mutant girl.
The final part of the trial will be to clear out the bottom of the abandoned sewer system, which has a massive Octopus in it. This isn't what you're after though.
With the help of a good team (you really need to have one person that can do good holds, one person that can draw aggro and tank, preferabbly a good debuffer or healer and some damage dealers) you can go down into the sewers and just hunt the Krakens. Each kraken will net you anywhere from 70,000xp to 45,000xp depending on your level. There are 5 krakens inside this mission, one at the very top, and then 4 sprinkled at the bottom.
Once you defeat the kraken at the top, have someone phase shift and go down to the bottom of the sewer to a small cave near one of the force field generators. From here, TP everyone else down. Now have the tanker go out and pull each kraken back into the cave where you hold it and kill it. Once all 5 have been defeated, have everyone in the team quit the team, and have the mission holder log out of the game. Everyone will then be booted from the map and sent back to the top. Mission holder relogs in and you rinse & repeat.
This mission lasts for 1 hour & 20 minutes. You will probably be able to get anywhere from 3-6 runs of this through. At the lower levels, one run of this mission will net you 350,000 experience and a shockingly large amount of influence. If you are on a good team and can do 5 runs, you're looking at 1,750,000 xp in under 1 hour and 30 minutes!
A word of caution, the path to the abandoned sewers can be tough. The best entrance in my opinion is through Steel Canyon. Having phase shift or invisibility is a huge asset. It's also considerably much more handy if you actually have this mission yourself. Gathering a team is never difficult but getting a good team together where multiple people have this mission is hard.