Yeah.... actually you quite nailed the cheapest & easiest means of transmission if the conditions are right.
Meaning there is a sponsor radio station covering the event, thus we already covered the transmitter. (But not cheap either, the radio station need a leased line, maybe satelite or tele line to tramit to their broadcast station). Then each speaker point just have a FM reciever installed, can already. But quality at best is at radio quality only.
In using Cat5e, per 300meters roll cost less than 100bucks. Basically just need a D/A cum repeater box at every junction. Quality should be as pristine as the source allows.
Heehee.... if you got any leads just look me up, we can work together on it.
Cheers,
Mike