Wind and currents are corrected for by what is called, set and drift. We are constantly correcting for set and drift and the helmsman has to use greater rudder angles to stay at the heading we want.
So set and drift is not at all a factor in this Jroa, that is easy to correct. Hell I don;t even have to do the math anymore, my electronic chart does it for me

Now Thinkingman brings up a good point. My gyro is keeping me at the heading I want, that heading I want based on the gyro is using gravity and the coriolis effect to correct what the gyro repeater is saying to the helmsman and me.
So now that Thinkingman (sorry thinkingman my post was a little misleading I already knew this just wanted to bait people into talking about it) explained how my gyro is working, how and why would my gyro do that on a flat plane?
Using straight lines on a flat plane is the shortest distance between two points, and the shortest way to get to where you want to go? So why would the Flat Earth map show that I am going to do a circle to get where I want to go. Makes no sense.
Now a short answer would be, because to get across an ocean to reach another piece of land you have to curve in a circular path. Now answer me this, would your gyro not notice that you are turning in this circle to get there?
I think it would, why would it not? My vessel is turning on a flat plane to reach another land mass.
I love it you all are so confused hahahahahaahaha