I've been steaming on about 7-8 hours a day since headstart (given a few days where I couldn't stay connected due to server issues) doing exploration missions in an escort and I'm only Lt. Cmd. 6.. and starting to get burnt out. Any quick leveling advice from the Admirals?

And please don't talk about taking your time to enjoy the game. This isn't really a game that has an enjoyable journey in the first place, but I'd rather get into my T5 ship and Roleplay/Explore for the fun of it (as opposed to exploring for progression's sake) with my wife.
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Aside from that, just do all the missions available to you and you should make Admiral fairly quickly.
I have played every storyline mission, etc, etc and just hit RA1 yesterday. Playing as Science, so it's not as if I am some sort of damage dealer.
Just play the game.. not hard at all to hit admiral quickly.
Storyline Mission coupled with a die-hard 2 exploration mission a level rule.
Truth be told, I was just having too much fun and then wound up higher level. Don't think about the level, just think about the storyline. Like they say, a watched pot never boils.
A watched exp bar, never bumps.
I did dse`s, mostly. Episodes too. And dont run from exploration missions where you need to take down enemy ships. They give nice xp too.
The exploration missions I avoid are "Relief Effort" (due to having to run back to Starbase for provisions) and "Investigate Research Facility" because for me the enemies are bugged and spawn much higher than my current level.
I am a Tactical Officer in an Escort with all Mk IV equipment. 2 Disrupter DCs and a Quantum Torp up front and a Disruptor Turret in the rear, with a Shield Array. I kill space enemies fairly quickly.. and do not die unless I get really unlucky with the unending Klingon torpedoe barrages, but that isn't very often.
On the ground the fights are a bit longer despite my heavy use of Focus Fire, Fire on my Mark, and Target Optics. I use Mk IV phaser weaponry for myself and my BOs.
So if you really want to hit end game that quickly that's the road I suggest as well, but word of caution for what there is for end game now you will be bored quickly and even when the 45 day patch comes I don't know how long that will keep you entertained so I say slow down and enjoy what you can. And for all of you who say we leveled too fast do you really think that when you hit Admiral there's gonna be tons to do? This 45 day patch with it's raidisodes also brings more of the Klingon content so it looks like we'll be waiting at least another month or two after that to get what should have already been there to begin with. Had their been more story line missions and more to do from the beginning maybe the leveling could have been slowed more, but imagine if we had to grind the same things even more than we already do lol, there would have been twice as much whining as there already is.
I'm not worried about having nothing to do at Admiral for the reasons stated in my first post
Pretty much it sounds like I am doing the right missions but am doing something.. wrong. Either I am not going as fast as I should be able to or I am getting bad luck with longer missions?
And show off your ship at the Earth Spacedock.
Oh, or you can horde credits in an attempt to buy all Blue or Purple Mk X gear for your ship.
Well many others have been saying its the content that you do. While this is true it also has to do with the ship and boff setup you're using.
From my own experience (I leveled 1-40 in 4 days even before the game was released) I found that using an escort is the fastest way to level. Get rapid fire cannon, HYT, and Jam Sensors and you can often take out a mob in 15 seconds without even being hit.
Do the actual missions quests and episodes. Do the defend sector and explore missions only once each unless you run out of plot missions. Solo, except for fleet actions and defend sector missions (or group with RL friends). Pugs are dumb, 40% of them are trying to leech xp, or won't stay with you, and the chat interface isn't conducive to trying to effectively communicate. If you're having trouble surviving ground combat, take two science officers with you with lots of healing abilities.
Took me 3 played days to RA2 that way, then I ran out of content. RA2-RA5 is fairly quick now though.
Some other tips: As with every other MMO, if you want to level fast have high dps and low downtime - regenerative shields that you can swap on (or keep on), abilities that focus on damage over survivability. 100% power to weapons for most fights, 100% power to shields in downtime. Don't go to full impulse unless your shields are close to full.
Don't be afraid to max out your boff skills. You get such and absurdly large number of boff skill points you won't know what to do with them all later. I've earned about 60k boff skill points and spent about 40k, 20k of which was foolish waste. And I basically stopped playing my main once I hit RA5 other than for dailies.
If you have to do exploration missions, skip anything that isn't in space, as the ground missions take longer, and force you to waste time zoning.
Ok so that's if you want to really minimize your levelling time, but some of that isn't all that fun. The control abilities, and defence stuff make you feel a bit more like you're actually trying to be a captain and not trying to die so you can heal faster. The 'aid the planet' missions aren't worth it, under any circumstances sadly.
PVP is only sometimes viable, so for leveling use it sparingly. The problem is that a single klingon vs 5 feds will just cloak, and then you're trapped hunting for a moving target for a long time.