Look for the following line (line 104) in Game_Player. (in the refresh method)
actor = $game_party.actors[0]
replace it with
#actor = $game_party.actors[0]
actor = $game_actors[1]
Now the Player graphic (on the map) will always be actor 1 from the database.
And the original line is still there, it's just a comment now. (for reference)