If you write and are actuall trying to change something why would you not use 'your precious day off" to clarify and convince. Either it is important or it is trivial but I know no line of work where you have the luxury to do everything on your own schedule or have the arrogance to believe you would.
I'll bet you'd go to HQ for a coffee and muffin with your mate, so next time agree to meet said manager at Costa, you might even get him to pay!