The rules say that level runs don't allow NG+, but how is that viable? Let's say I want to run Starscream's level but mess up. Do I have to run through the entirety of the prior levels in a new game save just to get back to it? And if so then what about savestates, are those allowed?

You can continue if you make a mistake during the run, it would be a lost time.
No savestates please.