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Last time I played this was three months ago and I was impressed by the potential. Now it looks like you've really progressed, so looking forward to dip in. 

As alluded to, my last save is 3 months ago (guessing 0.1.0)...Do I have to start a new game (and even if I don't have to, should I anyway?)

You don't have to start a new game, but for the next update you'll have to.
It's not needed to start a new game!