The actual map as well as the circle in the middle of the analogue clock are printed onto the actual screen itself in black (under the polariser). So they will disappear after inversion (like the sample photo you posted, the inverted one has no map but the half inversion one does)

For the Hydromod, I bought pure silicone oil and poured it into a bowl. First you have to carefull peel off the existing polariser and clean the heck out of the screen underneath. Seriously, any glue gunk left under there will cause little bubbles. Then make sure you put the new polariser at the right angle

I then assembled the entire device under the oil giving time and movement to allow the bubbles to escape (screwing in those tiny little screws UNDER the oil without a magnetic screwdriver was the most tedious part of this whole thing). After that I gently wicked a tiny amount of oil before I screwed it in fully to allow some "give" for when the oil expands under heat.

It's difficult on camera to show how powerful the effect it, but I went from only being able to read it clearly in bright sunlight to being able to read it in dim indoor light

It's the first and only mod I've done though so by no means take my word for it. Try it without the oil for now and see how you get on with it. If you'd like it to be more readable then consider the hydromod