It looks like indeed there is no overland road to Bamaga.
https://youtu.be/l_sY-gp_pqg?t=228
If you hit such roads in the wet you're going to get bogged - and extracting yourself from wheel deep mud is an arcane artform.
Fishing & 4WDing in West Cape York: https://www.youtube.com/watch?v=sB3ia158GOI