"I know the Map feature will populate the GPS field for all selected images when I right-click at a certain spot on the map. However, it seems LR will not let me add additional images to the same coordinate position used before."
The Map module has long been a buggy mess on Windows. There are two methods that sometimes work:
1. Select the photos in the filmstrip and drag them to the map, positioning the bottom tip of the map pin you're dragging exactly over the bottom tip of the map pin on the map.
If you're on a higher-resolution display with Windows display scaling set to larger than 100%, then a longstanding bug drops the dragged photos away from where you positioned them, so you can't use this method. You used to be able to drag an existing map pin on top of another, but that's now broken.
Drag and drop one new photo to the map, then reposition its pin on top of the desired pin. The Map module has never let you reposition pins that have more than one photo assigned.
2. If the existing map pin on the map has just one photo assigned to it and you have at least two photos selected in the filmstrip, then right-click the map pin on the map and do Add GPS Coordinates To Selected Photos. You can't hover the mouse for very long over the map pin before right-clicking -- otherwise, LR will show a thumbnail of the photo. See the attached screen recording.
A LR bug causes Add GPS Coordinates to not appear in the right-click menu if you have two photos assigned to the map pin or only one photo selected in the filmstrip.
3. If the existing map pin has more than one photo assigned to it, there isn't any way of dragging or right-clicking to assign the same coordinates to new photos. You'll have to copy and paste the GPS coordinates in the Metadata window.
Update: I corrected methods 1 and 3.
Update 2: I corrected method 2 to explain the bug with Add GPS Coordinates.