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Would a treadmill be safe at that pace? 13mph is extremely fast especially over a sustained period of time.

Here is Haile Gebreselassie demoing a 4 minutes per mile pace on a treadmill: https://www.youtube.com/watch?v=YSp1r1QhUSY

I don't know how safe it is, but people have done times in that general speed range, e.g. Eric Blake's 2:21:40: https://www.recordholders.org/en/list/treadmill.html

2:21 is not even in the same ballpark as <2:00. 2:21 is a very respectable time, but not even international/national standard. It's a chasm.

When you're talking about treadmill speed and the mechanics of that (which we are), it's definitely in the same ballpark. In terms of running, no.