In a previous entry, I indicated that Google Maps does not place markers precisely in response to a search using high-precision coordinates, and that it sometimes places a green arrow at the precise location. In fact, it always places a green arrow at the precise location, but unless you zoom in sufficiently, it will be hidden behind the red marker. So, it's not necessary to have Google Earth to find the precise locations, as I indicated in a previous post. The erroneous statements in the previous entry have been deleted.
So, to create and save a map with precise markers, do the following:
A) sign in
B) enter the My Maps mode
C) perform a search using high-precision coordinates (which creates two temporary markers: a red marker in the vicinity of the precise location, and a green arrow which marks the precise location and is often hidden behind the red marker until you zoom in sufficiently)
D) click on "save to"
E) in the pull-down menu which then appears, either select an existing map, or create a new one
F) click on Save
G) A notice that the location has been saved, followed by a "View map" link to the map of interest, will then appear above the map-window, under the search box.
H) Click on the aforementioned "View map" link
I) The map of interest will then appear, with three markers associated with the location just saved: a red marker with a blue marker essentially on top of it, and a green marker at the precise location (it might help to click on the newly-added location in the list to the left of the map-window).
J) Click on Edit
K) Drag the blue marker to the precise location.
L) Move on to the next location or exit the Edit mode.
It might be necessary to deviate from this procedure, depending on various factors, but it should help you get oriented.