Re run the first 4 Devidian missions over and over. If you have a 3 or 4 man team all 4 episodes can be done inside of 30 minutes. Do the 1st and 4th missions and turn them in and then run the 2nd and 3rd as both require a trip to the other station to turn in the missions. The 1st two you did are about ready to be replayed.
Also, the skill point boosters are a nice bonus. Try this ( don't leak it) run all missions you can but never turn them in. my best was 31 missions completed but not turned in. activate a skill booster and then turn in all missions and it somehow gives them all the 20% boost. Hush Hush now, but it will def help raise you faster. You make 9 levels and the 10th level is freebie basically. Also try running them on elite as the kill points are greater and I did an entire level off npc kills.
If you want to do missions, it is fine but consider this....
Most missions are a combination of space, ground, and then space scenes taking about 15-30 minutes and giving you 300 xp. If you were to speak to Lt. Antenone who gives out explore nebulae...he gives 50-100 or so xp for doing 3 explores in nebulae. You get 120-180 xp for each explore you complete plus the reward xp. If you do nothign but space explores, you can finish those in 5-8 minutes. Doing this 3 times can take 15-20 minutes giving you 100-150 more xp than the story missions / mission replay.
If you want to be able to find a fast way to get space explores, I have a pattern for you to follow...contact me in-game or in mail so I can better facilitate your needs.
I am going to give this a try, if you don't mind. Leveling a KDF toon myself right now and I have been stuck at LT CMDR for a while now.