I think the drive from SYD-MEL via the coastal route is a great idea. I did this trip in about 5 days in October 2017, and really enjoyed it. There are some absolutely beautiful spots along the way. I actually started in Newcastle, so starting at SYD airport would be a bit quicker. November is a perfect time of year to do the drive as well.
Yes, you can fly anywhere from SYD and probably direct to MEL from that place, but sounds like you are spending enough time on airplanes as it is! If you don't mind driving, this is a great chance to see some overlooked bits of Australia.
Here's my itinerary suggestion:
13th: Get a hire car and stay at the Rydges Cronulla Beachside. If all goes well you'll be there before the sun sets, and it beats any airport hotel.
14th: Get breakfast in Kiama (1 hr drive), then tour down the coast to Vincentia (another hour) for your overnight. I stayed in Dolphin Shores, a pretty little motel.
15th Tour around Jervis Bay, Hyams Beach, and do a whale-watching tour. Jervis Bay is one of the prettiest parts of Australia IMO. Drive to Merimbula or Eden (detour to Tilba-Tilba for a quick look). (3-4 hours)
16th: See the Eden Killer Whale Museum if possible, it is excellent. Check out Ben Boyd National Park. Drive to Lakes Entrance (3 hours), you can side trip to Mallacoota but I'd give it a pass. Beautiful beaches at Lakes Entrance.
17th: Take the ferry to Raymond Island (lots of wild Koalas to see here). Drive to Walhalla, and old Gold-mining town. Stay here or nearby
18th: Drive to Melbourne
Driving distances are only around 3 hours per day so plenty of time to look around and do activities.
Here's my trip album from a similar trip, although it's basically Newcastle to Lakes Entrance (then I went straight home to MEL. All the photos are geotagged. (Having some problems with the preview, so just use the below link and click on the 'Grand Pacific Drive' album.
https://www.flickr.com/photos/14999805@N06/albums/