Can I start a new game without wiping the old game's saves?

Yes you can. You can basically start a new game whenever you want through the main menu. However, note that if your original game is only saved in the autosave, then you risk losing it by starting a new game.

So, how to start a new game without wiping your old save games (per instructions from the OPs link):

1. Enter your old game and trigger a save (eg complete a mission)
2. Turn autosave off
3. Start your new game
4. After completing a mission in the new game, save it to either another profile or save slot
5. Turn autosave back on

You should now have 2 save game slots, one with your old game and one with your new game.

Source (final answer in thread)