In the Coliseum, how do you deal with opponents using sword beam outfits?

The Sword Suit and Sword Master Suit let Link fire sword beams while at full health. After several Coliseum matches against players using these outfits, I can't help but feel that they're strictly superior to any possible other strategy for the mode. The beams can be spammed indefinitely until you take damage, aren't restricted to orthogonal+diagonal paths (so there are no "blindspots" like arrows and such have), and even if you can take the guy out, his health gets refilled and you have to again waste a lot of health doing a bumrush to try and poke him once. This isn't even to mention that their swords deal double damage, and in the latter case, also have double range. (And there's also the Fierce Deity outfit that shoots beams in four directions at once...yeah.)

Is there anything that can really be done about this? Even if the two remaining players unofficially team up against the one sword suit guy, he'll back himself into a corner of the arena so there's not enough room for A to get around behind him as he attacks B. Fighting fire with fire doesn't really work either, because whoever gets the first hit pretty much wins, but doing so is basically a crapshoot. Fireballs get reflected without effort, bombs can't be carried without being hit, and all other items are too slow and/or lack 360-degree aiming (not to mention that just finding and collecting any item is several free seconds of target practice).