I prefer to replay from the basic game start,
I do believe it's an excellent idea, from a player's point of view.
but I never saw an option for New Game+.
After you've defeated the boss, whenever you get the chance, go to the Save menu, check out your last savefile, should be displayed "New Game +".
Nor did I see individual stats info after the game stats window.
No Main Menu?
So, I did some exploring and found that New Game+ option appears when I loaded the game from that specific save slot only.
That must be it!
However, how do you restart this game from the original, fresh beginning?
What do you mean? If you mean the savefile after the boss is defeated, there is nothing else to do...
Do I need to delete the save files and reinstall the game?
I don't think so, not at all.
You should be able to access NG+ from your savefile AFTER the boss has been defeated.
Or else you can just start a brand new (and regular) game.
There are only these 2 options.