That's not a great analogy, 2WL. The issue is not in the manner in which ones gets beat; it's an issue of artificially extending the same.
A perfect game in baseball can happen in the natural progression of a game. Indeed, as one can infer from the name, a perfect game is the most desirable outcome one can hope for. And, let's not forget, a perfect game has the effect of shortening a game, in terms of length. A perfect game means that one team only faced the minimum 27 batters, and the more batters you face, the more time it takes, of course.
The game should take as long as it takes to reach an ending, and no longer. If a stalemate is reached, and nobody is willing to change alliance structures, then the game should be drawn and concluded. If a person is able to reach 18 centers, they should take the win and conclude the game.
Anything else is going against the spirit of the game and the win conditions. It makes the game take an unexpectedly long time, and a person should be made aware ahead of time that this is a situation they are getting themselves into, just like any other special-condition game people have.
The main problem is that the losers have no recourse here. The game is over, everybody knows it, but they are all forced to sit there submitting blank moves every 5 minutes until the victor gets bored and decides to finally end the game. Whether that be 5 minutes or 5 hours depends on one person alone.
Perhaps a resign feature would be useful. It could be a vote button just like Draw and Cancel. In this case, when all but one remaining player has pressed the button, it awards a solo to the person who hasn't pressed it. This will allow players to end a game they know they lost, and it will prevent abuse from players (regardless of whether or not this particular situation was abuse, it's undeniable that this situation could be abused).