Would you drive Broome-Perth-Sydney and to Cairns in 3-4 weeks? Also 6000 miles with detours.
You're packing too much imo. Driving from San Francisco (or Los Angeles) to New York can be done in 3-4 weeks but even then you're missing tons of remarkable sights. Nevertheless a cross country drive is everybodies dream. So please make up your mind first re starting and final location. My advice: Start Los Angeles re Las Vegas and GCNP and leave from New York. Or start Las Vegas. (Or in reverse of course)
Yeehaw