I know this is a common thread for the PvP group to focus on but I thought this could be a lot of fun for PvE as well. In fact if the system crosses both PvP and PvE you get a major benefit from the design instead of being focused on one small aspect.
Obviously one of the most appropriate enemies for PvE conquest is the Borg. You could have them appear in the North West, above Sol where nothing has been developed. Their goal is Earth of course. You could give the other Factions like the Klingons focal points to start from as well. Considering the Borg are a major threat to all life it is an enemy of my enemy is my friend situation. Those details can be worked out any way you want, as I don't care.
I am sure there are folks who have designed many conquest battle map ideas. My suggestion though for the PvE map is to have focused singular targets where players gather. Such that the fight is in one or two areas you can choose from. At the finale to make it sort of interesting all the factions could fight together against the major big bad guy. Success might be defeating it and failure would be the bad guy gets away to fight another day.
The battles should be more about endurance. Such that you go into a system and you have to battle there and hold it for say an hour of game time. It isn't expected that players will stay the whole time. There are missions that you have to keep doing. Basicallly it is a battle of attrition of sorts to see who is the loser. At which point you hold the ground and the borg move on to another target or lose the area and players have to move to defend another region.
It should be a pretty big battle all the time with NPC's filling in when players are not present. Obviously NPC's would be sub par but add to the Star Trek feel of eye candy explosions compared to the player ships and crew that seem to survive when others do not.
Some fun things with an NPC conquest like the Borg is assimilation. You could have it that players can be assimilated and assist the Borg. It probably would have a cooldown such that they only have a few minutes to play as a Borg and earn special reputation points. Obviously this would be mostly focused on avatar combat instead of ship.
A space battle and a ground battle waged at the same location would also make sense. Having the players feel spread to having to go into space and back to ground and so forth would add to the dramatic feeling of desperation. So they might be doing well on the ground but the space side needs helps so now you have to decide if you stay and help on the ground or lose the space side.
Choices like this would be a lot of fun. Finding a way to balance it and bring lots of players together for these battles would be a challenge but I think people would enjoy some sort of gameplay like this.
Again I mostly mention this idea as I figured it would assist in the development of the PvP conquest ideas if they can also be applied and used for some sort of player versus enviornment situation. I would love to participate in a full scale stop the Borg invasion situation.
Now if you guys are even more creative you could use the map for all types of enemies, not just the Borg. So after the Borg are defeated, eventually a new threat emerges instead of the same ones appearing. The gameplay wouldn't change to much but the enemy would be a bit different so it feels less repetitive. This way players don't say, "Oh look the Borg are invading again..." It's probably better to hear, "Looks like the Borg are trying to invade again we just stopped the Strekkelan threat!"
Anyway, long winded post that I am sure some other players have already mentioned in far greater detail at some point in the past. Either way it might give some of you pvp conquest types something to think about when you suggest PvP systems that might also cross over good for large scale PvE as well.