Could you delay the large screens, commentaries, and live broadcast by 3-5 seconds (or more) such that any information gained from leaked noise would have minimal impact to the players? This would make ANS headphones viable
Sound proofing however still doesn't solve the issue as it doesn't deal with the vibrations in the venue. Pro players have commented that if they start feeling vibrations while 'farming' alone, they become more cautious - asking a support player to cover the gank or move to a safer area.
But I had to look up MOBA too :-)
And I used to write multiplayer battle games for a living! And my favourite recent game was a MOBA without me knowing that was a term! Which goes to show, times change, words change, and it's easy to live outside gamer subculture, even while playing.
So what's the MOBA that got you interested even though you're not familiar with the genre?
Aeon of Strife being the first one from 1998.
In internet comments, if you're not really specific with your words it's likely at least somebody will misunderstand your intent, partly because they can't read your mind and partly because with so many potential readers the odds of misunderstandings goes up.
Riot tried this with League of Legends and the result was that you'd get players jumping up celebrating 30 seconds before the audience saw the nexus falling, which was incredibly anti-climactic.
Imagine if you were watching tennis and halfway through match point you suddenly see the player celebrating.
To be fair, most of the time it's GG well before the nexus actually falls, but it's sometimes meaningful, and it still ruins the moment to have that sudden de-sync effect as you see live players reactions before you see why on screen.
As a result, as far as I know Riot abandonned having any meaningful and deliberate delay (There's still some technical delay natural to broadcasting).