Mainey I don’t know if this helps, but it is all I know.
I know the road from Normanton to Kowanyama, normally a reasonably good road. I know the locals go from Kowanyama to Pormpuraaw, but it is a seasonal road, I have never done this road so it is only on hear say.
I don’t know of a direct road to Aurukun from Pormpuraaw, although I have traveled from Yarraden, which is south of Coen, to Aurukun, they used to have a barge to go from the south side of the Archer River over to Aurukun, but this was some years ago, and the conditions might of changed.
I don’t think there is a road to Weipa from Aurukun, other than going back to the main road and heading north.
This map I think shows the roads I am thinking about.
http://www.derm.qld.gov.au/cape_york/pdf/map.pdf