Spanner, I rode that way last year. Tackleberry signed me out of a servo in the outskirts of Townsville about 12:30 am. I calculated there was no point leaving any earlier because I would arrive in Hughenden and Richmond long before the servos opened.
My recommendation is to leave Townsville at 12:00 am, refuel at Charters Towers, arrive Richmond approx 5:30am. (12:00am + 5:15 riding + 0:15 refuel CT). Google times are conservative but you are riding at night through roo-infested areas. You should easily make the 359 kms between CT and Richmond without carrying fuel.
If you leave Richmond about 6:15 am and take about 15 mins to refuel at Mount Isa (406 kms in 4:23), Camooweal (190 kms in 2:05) and Barkly Homestead (260 kms in 3:09); then ride to TC (211 kms in 2:29) you should get there before sunset (subtract 30 mins time difference). This is where you can do better than Google times but keep your eye on the fuel guage.
I’m not familiar with the extra bit you’re doing out of Townsville. If you’re going to deviate from the shortest route you need to provide “corner” documentation, fuel receipt, ATM receipt, cherry ripe receipt, etc. Check all receipts to ensure they have the location and correct date and time.