When I first mentioned adding the classic "beer & pretzels" scenarios of the genre to multiplayer I had actually mentioned a couple other scenarios but quickly cut the list to "The Big Three" of base defense, capture the flag, and space hockey. Here are all the other "beer & pretzel" scenarios that I can think of at the moment, I am sure I am forgetting a few, but this will provide a more complete set of options to choose from should they decide to do this. They might like some of these better for their game for reasons I can't know because I don't know their game yet. I particularly think the "Rabbit Chase" zone would be particularly fun with only 6 players.
All of these concepts are from either Star Fleet Battles or Subspace, the only two spaceship games I know of that ever made scenarios like these...
Free For All/Every man for himself - No explanation needed here.
A couple forms of capture the flag...
Teams work together to capture a number of flags. Flags appear randomly on the map at game start and are picked up by flying over them. The moment all flags are held by a single team, a 3-minute timer starts (the game’s theme music or some other music during this time would add to the tension). The team must hold all of the flags for 3 minutes to win the game. When a ship is destroyed, that ship “drops” all flags it was carrying. Each flag carried increases all of that ship’s inherent charactaristics (speed, turn, thrust, energy recharge) by 10% for each flag carried . This is essentially Subspace’s “War Zone”.
Stationary flags are fixed on the map inside of a base-like maze with only 2 or 3 ways in and out. There are two teams. Running over a flag changes ownership to your side. When all flags are owned by one side a 3-minute timer starts, that side wins at the end of the 3 minutes. This zone is essentially Subspace’s “Death Star Battle Zone”, which is really just the “King of the Hill” concept.
Rabbit Chase - There are no teams, this is an FFA scenario except... There is one portable flag on the map. The player who has the flag receives huge bonuses to all aspects of ship performance (i.e. a “super ship”). All other players are attempting to take the flag. This is based on a concept inspired by Subspace's "Jackpot" zone, but slightly altered to work with a low number of players. I never thought the name "Jackpot" made any sense for this, and have always called this idea "Rabbit Chase". This was a perpetual, never ending zone in Subspace, a means of someone "winning" could easily be established to create an ending. [EDIT: I've actually realized that this scenario actually originated in SFB, not Subspace, this is SFB's "Juggernaut" scenario concealed so well I had never noticed it until now.]
Circle of Death (A.K.A "The Admrial's Game" & "The Forbidden Scenario" due to it's original form of being an illegal SFB game played by SFB insders for money at conventions.)- From SFB. 6 players. Each is targeted on one of the other players. That's all they know, they don't know who is targeted on them. Shoot any ship other than your target, or the person who is targeted on you, and you are out. Have fun:-) This is one of the most popular "beer & pretzel" scenarios in all of SFB and playing it as the "side game" for people knocked out of tournaments at conventions was something of a tradition. It has never been easy to find 6 SFB players in one place, so... 
That's MY Freighter! - Also from SFB, probably the most well known and popular "beer & pretzels" scenario in SFB. This would work exceptionally well in SC. A 3 player scenario in SFB, the 3-sided 2-player teams variant is also very popular (and even better). 3 "starting zones" at map edge in triangular pattern from the center (in SFB, these "zones" are six hexes across). Player starts in map edge zone. Object (a freighter in SFB) at map center. First player to tractor object into his starting zone wins. Ships don't need tractor beams, in SC this could be an automated effect. Get close enough, you tractor object. Must "stutter" while towing, move too fast and you will separate from object, leaving it where it was at that moment. This is actually just another form of capture the flag.
These are all the "truly great" ones I can think of right now, and probably almost all of the truly great ones. In addition too the "The Big Three", I think Rabbit Chase and That's MY freighter! lend themselves particularly well to SC and 6 player max in multiplayer.
EDIT: Oh, the second, "Death Star Battle", CTF game above is, at the same time, a base defense zone. In fact, it was my favorite base defense zone in Subspace (which had several different versions of base defense zones, which were the most popular type in that game).