Belden 9451 can be found as cheap as $179/1000 foot roll. It's thin, easy to pull, good quality cable widely used in commercial, fixed installations for line level audio signal.
If you're the rink's audio system advisor, I'd highly suggest "talking them into" running a dedicated line to each box.
A "patch bay" isn't necessary, use screw terminal strips to land all of the individual runs. Do it in a concise order and label things clearly. Run another cable from your head end, which it sounds like will be a mixing console of some kind, to the first terminal strips and then make short jumpers from there to each cable used. This is a cheap and effective method that does not require a ton of connectors and patch cables. Screw terminal strips are cheap. Just remember you'll need 3 poles for each run when you're designing your audio signal path and ordering the strips.