...Is there any major problem with a Swiss? It handles dropouts, allows people to play multiple rounds even if they don't win, matches players by ranking pretty decently pretty quickly (round 3), allows for people to skip rounds if needed (byes).. and allows for people to get recognition for winning a rating section (Open, U40, U30 or something).
The main problem is that Swiss pairing is a lot more calculation intensive, and, frankly, if there's no online tool to make it work and make it easy for people to see their next round opponent.
In fact, I can't find a free program at all that will do that. If anyone can, then maybe we could run a Swiss tournament.
It's pretty hard. Certainly there are no generic, free, and polished ones. http://www.twinfeats.com/tf/twinfeats/Java/pairings/index.tfs
this may help, but has some of the bells and whistles needed for a Chess tournament that obviously might not apply to dominion.
On the other hand, Swiss tournaments are comparatively easy to just do in an Excel sheet or something, not really that much harder than a round robin. Divide into brackets by #gameswon, split and pair, improvising when there is an odd number in a certain group (Lowest rated in group 5 wins plays highest rated in 4wins, etc.)