Thanks for the feedback!
You've touched upon a small technical nuance of web-based interactive maps.
The way the map recenters and zooms is essentially a side-effect of displaying the info window (balloon) for the selected station. Web maps cannot "float" their balloons outside of the rectangular region where the map is drawn, so whenever balloon text needs to be displayed, the maps will recenter themselves to make it all fit inside the map frame.
As a partial work-around, you can close the info text by clicking the "x" in the upper right corner of the balloon. This makes the balloon go away, but keeps the coverage overlay on the screen. If you then zoom in to your marker and drag it around, the map doesn't move because the balloon is no longer jerking you around. The numbers below the map will still update when you change the location / height, and the map will stay still.
I think this will help you achieve what you set out to do.
One warning though, if you click on another radio button, a new info window will be drawn, and your map will be repositioned to make it visible again.
As another suggestion, you might want to try the Google Earth overlays instead. The web-maps are quick and convenient, but they have lower resolution than the Google Earth overlays. For "poking around" neighborhoods, the web maps might not have enough resolution to see local details. Personally, I find the 3D representation in Google Earth a much more fun and intuitive way to "see" signal coverage.