TLDR; Allow cross faction grouping and queuing, cross faction housing, and add a new capital city in a neutral area to get them face to face on a regular basis. Faction v faction pvp flagging (with the exception of parties) and faction capital cities will remain unchanged.
Personally, I think the faction barrier should be dropped to some degree. At this point, it is mostly just splitting the population into two halves that can't really see each other at all. Lore wise, the story has been very focused on making the entity and strain the main enemy, so the factions cooperating to take them down could work. As to how this could or should be implemented, that would be a bit more difficult.
One of the main things keeping the factions separate at the moment is the geography and convenience of the capital cities. Let me explain. Everything that a player needs on a regular basis is in their own capital city, everything from auction houses, to crafting tables, contract boards, vendors, and more. Not only that, but for many of those things, the only place to access them is in the capital, causing the players to just bunch up in their faction zones on the literal opposite ends of the world. How can we fix that? Well, we can add a new capital level city with everything a player needs (crafting, ah, cx, contracts, pvp vendors, raid vendors, world teleporters, faction specific teleporters to the existing capital cities, etc) on one of the two neutral continents, either Isigrol (more likely option) or Farside (more fun option). This is starting to veer more into hypothetical territory, but these are just my ideas. The city itself should be home to one of the neutral factions such as Protostar or lopp. Flagging will still work in the city like it will in open world and the guards are normally friendly/green towards players. However, dealing direct damage to another player will aggro the guards. (so a player who is standing next to a guard and gets attacked without fighting back, will not be hit by said guard, and you would need to actively use an ability on your LAS to deal damage to get attacked) with the exception of duels (no guard aggro).The currently existing faction capital cities such as Thayd or Illium will still function as they are now with guards attacking the opposite faction on sight. In terms of guard coverage, patch up some of the holes in Illium to be more similar to Thayd in coverage, while the new city would be roughly the same coverage that Illium has now.
As for player to player relations, disable alien chat and allow players to do some basic social and grouping things such as partying up, dueling, and maybe circles (guild may be a bit much, as having the ability to freely attack guild mates may cause more headaches than needed). As for flagging up in a party, things will act normally from player to player, but disable damage and enable healing between party mates, but also be able to damage players who attack party members. For example, an aurin slinger and a draken warrior party up, they are both pvp flagged. They cannot damage each other, but the aurin can heal the draken as a friendly party member. A pvp flagged granok runs up, he is still friendly to the aurin, but is enemy to the draken. The granok attacks the draken, the aurin now sees the granok go from friendly/green to neutral/yellow, the granok still sees the aurin as friendly. This gives the aurin the option to save their draken friend by attacking the granok, going to hostile/red, however, does not give the granok the option to just throw something at the draken if they want to grief the aurin, even as a fellow faction member. Lastly, link the housing networks so player can visit whatever plot they want. This was in discussion a while back with pretty positive opinions on it.
Last thing I want to talk about is instances. It is pretty simple here, allow random queues to put members from both factions into the same team or party, however, give a checkbox option for "match me up with my own faction", similar to the old button to match players up with members of their own realm. Parties and raid groups will function exactly as they are now, with members of the same party being put onto a team in bg's, be put into the same dungeon or adventure, or be able to walk into the same raid id.
This is personally what I think would be the best scenario and it might be overwhelming if tried to do all at once, but it still maintains some of the rivalry between the two factions while simultaneously giving players more face to face interaction with the other faction and the option to do more activities together. I personally think that making a neutral capital would do the most to bring the groups together, even if it may be what takes the most work to put together.