Yokosuka wrote: An official mail giving the choice to the backer "keep your current rewards or choose AI battling+high ground as your reward" would be a brilliant idea, with real time calculation of the extra saves. With something like "If at the campaign closure we're still unable to reach this stretch goal, you keep your previous rewards instead."
As interesting as your idea sounds (for ultra fans like a lot of Dojo posters) I think this would cause more bashing from the medias and a bad publicity. Just look at how the Paypal campaign was reported by some media (they got 6.3M$ and now they ask for more), and let not talk about the interpretation made about Suzuki's "I could do with a little bit more of money..." from the same "journalists".
The best option in my opinion, is to provide access to upgrades for the Kickstarter backers.
If you look at the numbers, 26'238 backers pledged for the digital PS4 version.
Upgrade to 60$ for the physical version with an exclusive Shenmue 3 phone wallpaper for paypal upgraders would significantly push the funds: 26'238 * 31$ = 813'378$.
Same idea with the 80$ pledge upgradable to 100$ for your name in the credits + exclusive paypal phone wallpaper:
Doesn't cost a lot and could give the Team around 40'000$.
And so on for the other pledges...