Ah, and therein lies the problem with LARPing. No one is trying to kill you.
The most effective attacks with a single sword are narrow cuts to the throat and straight thrusts inside the pelvic region and below the ribcage. Since lightsabers don't let you bleed an opponent out, but do cut neatly through just about everything, the attacks against the throat and torso are likely to be the most fatal.
You never swing high or low when fighting someone with two swords, since they'll do precisely what you described there. Instead, you keep your weapon centered and focus your attack against their centerline, where it is impossible to properly defend with two swords. There's a very good reason that no one ever fought with two swords in real battles. Germanic longsword techniques and Japanese katana usage is the most effective demonstration of a single sword, while certain Italian fencing techniques make good use of a defensive dagger in the offhand, but never two equal-length weapons.
Also, as an afterthought: a single sword gives tremendous leverage when you properly use both hands to control the weapon, and allows you to change angles much faster. Holding two swords inevitably leads to wider, sweeping attacks that lack the acceleration of a single blade.
They don't have to defend, just attack you first and force you to take back your attack, or move away with it.
Real dual sword is pointless because it's not good for chop, only stab, but lightsaber is different.