Undrave
Legend
There's be no way to really track the distance covered over any number of days, and with a winding river it would be really hard to even tell the general direction you're going. Especially through a dense forest.
That's what using the stars and the sun as reference points is all about.
Though, it doesn't actually matter that much, if you're following the river, what direction you're going in. what's important are recognizable landmarks.
Heck, the public map might just be a series of straight line of varying size (or color coded for depth?) that branch off the central main river with series of points on the side that act as landmark. A bit like a subway map while on the train. It might make note of tricky curves and rapids, giant rock formation, man made landmarks, etc, and you only need more precise map if you're going to be walking off the river. If there's a section where you have to go through the woods to get passed a waterfall, maybe the public map has an asterisk that say "See local map 25" or something for that specific area and that map is the one that had more effort put in it.