Like I said, a sector that is about 2 sector sizes in campaign seems to be reasonable enough for a game that lasts 1 hour. Think of it more as a mini coop campaign.
Hmmm, you have a point with the node/system rush and farming problems. But I think it can be circumvented by timed events... To stop farming, nodes will usually just have 1-3 chain of events then after about 20 minutes, a node that's empty or depleted can be restarted.
I do not think clustering of nodes is fully required, nor large sector sizes. On the middle of the map, points of contestion will occur at Stores, which will become valuable mini bases because traveling all the way back to the base can take too long and be perilous. Now that you've mentioned it, maybe it's best to remove Sector Skirmish as a game mode, because Conquest and Escort have objectives that would most likely push the players to move out instead of farm.
As for team size... maybe the sector size will be 1.5x a normal sector if it's a 2vs2 game. And reach as big as 2x or 2.5x if a full 6vs6 match.
The game however will limit the player from fully upgrading the ship as compared those of the campaign... Probably you'd go as far as 2-3 added weapons and about a dozen system upgrades. Be hinted that this multiplayer's span is 1 hour while the usual FTL campaign lasts 2-2.5 hours. What you'd get instead is combat with what the player's can scrounge up for the next 30-45 mins before enemy players finally appear at their sensors. If you really want a powerful ship, you'd need your team to pool up their scrap and offer them all to one player.
As for the combat I've suggested, it really is not perfect. And you'd expect the outnumbered player to make a jump for it or at least destroy one and then jump; or hold long enough for reinforcements to arrive (we do have those occasional situations wherein ship combat becomes a stalemate). But my objective here in my original suggestions is to present a multiplayer game which maintains the roguelike feel instead of just prefabricated ship encounters.
It's not truly designed to be competitive, rather it's more of a new and different experience, with the campaign's development not only reliant on one player but on other players as well.