Agreed, if all you're after is the minion, just run it with Duty Support/Trusts - yes it might take a little longer than simply having a player party to 'cheese' through it, but the trade off is you have to compete with three other players for the minion potentially, assuming it even drops.

Incidentally, I got the Starbird on my very first run through the Dead Ends as part of the main scenario (I did it with Duty Support), so it definetely works (and I've seen it drop plenty of times since). Insisting on running it with player parties just to get the minion is unnecessarily complicating things (and this works for the other dungeons too - all EW story dungeons feature a minion drop).