Are you sure it's the compressor or just the compressor drive belt which also drives the power steering. The belts scream when worn. Try rubbing some wet soap on the underside (pulley wheel side) of the belt.....with the engine off. Start engine and, if the noise goes, you'll know it's the belt - easy fix.
If it is indeed the compressor, how much $$ is an unknown but, if all else fails, try the local Mazda dealer for a quote as guidance. Give the finger to, and turn your back on, any of these pricks who start with the \"sports car - difficult - expensive\" BS

. It's a modern Japanese car in mechanical terms and that's all there is to it.
RACQ (member?) might be able to offer some advice too. Let us know how you get on.