No, each waypoint is 48x48 pixels and the center is in the middle of that square. I won't bore you with the technical issues, but it's a bit confusing with the flag icon. This is the same with the flag icon on Garmin devices and software, from what I recall.
You could change the default symbol to a dot to be more accurate, then re-import your Garmin waypoints. To change the default, edit any waypoint and click on the icon. Click the gear at the top left of that window. Now you can choose your default symbol.
BTW, if you click on each waypoint you want to change, you can use the button to update the elevation, then save it. When finished, you could export the waypoints as a boydsmaps (.txt) file. This can be directly imported into Excel. But maybe that wouldn't be compatible with the system you've already developed?
The other thing to understand is that the LIDAR elevation data is equivalent to zoom level 17 (1.2 meters), so zooming in farther won't give you more accurate readings. If these are waypoints you created on a Garmin GPS, they are typically only accurate with 5 meters so zooming way in isn't likely to help much. There are going to be quite a few elevation readings within that 5-meter circle of probability.