In answer to whether I know how a sundial works, we made one in third grade as a science project.
Do I know how to make one that is accurate for a particular location for the entire year? No, but you can look that up in wikipedia. Do I know WHY a sundial shows the time and that it CANNOT BE AFFECTED BY TREES ON A MOUNTAIN somewhere beyond the horizon or even close to it? Most definitely yes.
The story says that the sundial had only stopped working for the preceding two years, so it must have been built correctly. Even according to the story the Baal Hatanya did not say there was anything wrong with the sundial. He said it was trees that could not be seen (if they could be seen they wouldn’t have needed the Baal Hatanya to tell them that the trees were blocking the sun!) that were affecting it. I have known since that science project in third grade that only if something blocks the sun the sundial won’t work.
As to your question: “And how would you explain the Gemorah (which doesn’t say how far the object has to be, it just says onc it begins to move something can block it.” You have not only shown that you don’t know how a sundial works, you have also known that you don’t know which Gemoro the story is referring to.
The only quote from the Gemoro in the story is “The Talmud states that at midday the sun is directly overhead”. That’s it. There is no reference in the Gemoro that once it moves something can block it. That was an alleged explanation of the Baal Hatanya. And it is so obvious that I’m beginning to wonder whether you were perhaps born in a cave and have never seen the sunlight and how the sun casts shadows.
Finally, a sundial displays the time in shaos zemanios, so “between two and five in the afternoon” means that the sundial allegedly started malfunctioning two shaos zemanios after midday and the began functioning properly again a sha’ah zemanis before sunset. If you can plant trees that will affect a sundial only at those hours you deserve a Nobel Prize in Science!