From the explanations of the official Roblox post, there is no way to easily change the starting place.
I think I got a solution to the above problem.
To make Place2 the starting place (and not lose the Place1 content), do the following:
- In Studio, open both Place1 and Place2
- In Place1, File → Publish as… and overwrite Place2
- In Place2, File → Publish as… and overwrite Place1
- Close all Studio instances and open it again