I'm sure something like this has been mentioned before but I think serious consideration should be had. The largest problems with PvP:
1) Rank separation causes low numbers per rank (the chance to ACTUALLY PvP is low and has long waits)
2) Impossible to balance against PvE
Each player selects from preset crafts from each tier to play as before the game begins. These 'classes' can be balanced easily in comparison to a player made ship which was designed with PvE in mind. This is also economical since nothing has to be tested against PvP before implementation into PvE proper.
Need proof this works? Examine DCUO Legends PvP. You can play it at any level and you don't need to worry about getting stomped by someone with more time or money than you. It's completely skill-based with no benefits to a player beyond their knowledge of the character. STO PvP would benefit greatly from this setup; it requires less resources (balancing is much easier without a bunch of unknowns) and can serve as a great framework to build upon. The traditional 'take your own' ship PvP would, obviously, still exist but I guarantee it would be far less popular.
Also, Star Trek never had fifteen Sovereign battleships fighting one another on screen so a six on six preset matches with three T2, two T3 and a T4 ship per side would be pretty awesome. All that is required is that damage across the ships be the normalized. The T4 has more weapons and a bigger hull but as long as per phaser the damage is the same as the T2 it is perfectly fine since there are 3 to match it.
Is it a perfect fix? No. But I guarantee PvP would be much more popular among players with an option like this. The proof is DCUO. It's nearly impossible to get into a normal PvP match but hit up Legends and you probably won't wait more than a few minutes on a long day. Any player could play it, no one would have a leg up on other players. Seems like a no brainer. Too bad good ideas are never popular.