Re: My SLAP Journey...
I started running at 8 weeks, as soon as my sling came off. It was kinda funky at the start as my right arm was still very stiff, so I had a weird style for a while.
I think running also helped my ROM a bit as it really gets things moving and the blood flowing, so in short I'd definitely recommend it.
As you mentioned, just don't fall over, at 8 weeks things have only just knitted back together so a fall wouldn't be good.