It is possible to get it done in teh public system, but you'll have to wait.
I think it's $3000-4000-ish, but depends on whether you have PHI also and what level of cover. I had mine done overseas and it was about $200 (score!).
In that case, yeah, I'd be asking why they're not working. Sometimes it is just ****ty luck, but it's always worth asking I think.