I wouldn't even bother making the player global. Just copy and paste the player into the layout you want just as you have it in the first layout but in the position you want it to start. Be sure to include the events for movement and such that you might have on layout 1 so everything's works. Also, consider making an event sheets with all of the player info that you can just right-click and include on every layout to keep you from redoing too many events.
You can also have an invisible object where you want the player to start and on start of layout, create player at said object's position. You can then also use that object's position for respawning on death, too. In any case, the player sprite must get placed in the layout somehow and you should include necessary events for things to work.