You can fly the lane of entry, even in a jab. Just can't go into controlled airspace, so watch the steps and stay out of class D (Camden, Bankstown).
I have phoned CASA to ask about the "jabs in built up areas and class D aerodromes". They said that Bankstown, Moorabbin, Archerfield (those named in the instrument) etc are specifically forbidden, however the others are left to pilot discretion as to whether it is "built up" or they can glide free, etc. With that then you would just need a PPL, and appropriately equipped and rego'd Jab. I flew into Sunshine Coast, which is class D, in a jab - no issues.
So yeah, you can take the LOE, just stay under the steps, and out of YSBK and YSCN. I like the suggestions so far of taking V1 South then hooking a right at Moruya - beautiful strip right near the beach and they have AVGAS, in case you need to stop. If you want inland instead, then from the LOE you can overfly YSCN (at sufficient height, and make your calls), then go down to YMIG, over to YGLB, across to Tumut then down to Jindy (you'll want lots of height, it gets a bit bumpy).
I've never encountered much around the Bindook NDB. What can be surprisingly busy however is Crookwell - seems to be a favourite for instructors to throw in diversions and Prec. Search n Landings.