Ideas choosing levels

We are currently discussing the idea of letting the player choose the level with buttons on the start screen. Here is a screenshot of the concept:

First you can choose "New Game" or select a saved game, and then the buttons for the timezone will be active and you can select to which timezone you want to go.

This would be cool but there is a problem with loading and saving the game:

1. Each level needs to be a separate adventure, that has no connection to a previous level

2. When saving a game, should be persisted which level you already finished?

3. It needs to be stored (globally) which parts of the time machine you already found.

What do you guys think of the idea?