I'm not saying that you adjust the speed for current because, like you pointed out in the rules, the courses are fixed to the ground therefore the ground speed must be used.
GPS speed control will always be "ground speed" unless there is something I don't know about the systems using a paddle wheel in different modes. I have never used GPS on the river so I can't say for certain.
Personally I would hate to be constantly adjusting the speed every time I turned around or for different sections of the river. Sloughs are slower than the channel because of the wing dams and the river is a living creature constantly changing in width and depth so the current must change with it. I know my wife would dislike me constantly reminding her to adjust for upstream , downstream or this section or that. Especially for trick or wakeboard where tenths of MPH are significant.