Honestly re loftus car park, not sure what month the football starts up, maybe call the team (can't remember the name that uses that oval). There's also Cricket there in the summer months..
Worst case, can have 30+ cars pulled over before the enterance to the National park, done it many times before!!
Another option, kind of off the track is Holsworthy train station car park - then Illawarra bypass to sutherland enterance!