I'm treasurer for a club in NZ which currently operates 3 582 powered aircraft.
It means: strip the engine down, replace all the small stuff - rings, bearings, pins, seals etc, check everything else including crank, put it back togethor, do it again in another 300.
Now, 300hrs is conservative, in a traning environment of course conservatism rules (although we do push it out to about 330), in private hands I think it would be fair to say that most 582s out there are run much much longer than that between overhauls (if they get overhauled!)
Cost wise, I budget about $3000 NZD (that's about $2300 AUD today) for the 300hr, some will be cheap, some will be expensive, but it averages out about right.
Is the 912 cheaper in the long run than the 582? Yes, it's fair to say it is (by how much I can't say, it's been a long time since we operated a 912 here and I don't have figures for it). Unfortunately with the 912 you have a BIG bill to begin with. Also bears mentioning that the overhaul cost for a 912 is also going to be significantly higher than the 582.
All in all, the 582 is a perfectly good aircraft engine, don't let the 300hr rebuild put you off.