The performers are miked, and using a PA - from the video it's clear the people doing sound are trying hard. I would not expect any form of stereo miking to produce quality much better than what you recorded. What you recorded was what it sounded like where you were. Moving to a better position would bring up the sound from the PA a little, but you're still recording the sound of an already amplified source - which rarely sounds 'special'. Depending on the facilities available to you, camera sound plus a stereo out from the desk will improve quality, even if the mix does not contain everything being played. If the organisers can include in the rider for the next event the requirement for a separate mix, maybe, just maybe you will get it - but even so, you're expecting the sound op to work for you when they're busy doing their own thing. There are plenty of multichannel solutions available, but even if you can record a clean feed of all sources, you still have to mix the thing - and if sound isn't your main area, this could be difficult for you.
I'm lucky, I can do these events, and mix them afterwards but the time it takes is not compatible with modest budgets. Equally as long as your edit time.