Personally, in my campaign so far, I've run it as follows:
Started in Nightstone, up to the point where the PC's free it from goblin occupation. But the back-story is completely changed: the place was initially attacked by Hill Giants, then hobgoblins etc ambushed the place killing a few people and dragging the bulk of them off into the forest as prisoners.
The PC's then went to rescue the prisoners, for which I used a slightly cut-down conversion of B5 "The Horror on the Hill". This has nearly been completed (most prisoners rescued, unexpected dragon killed, alliance forged with hobgoblin king), and the PC's are 5th level. I've enjoyed that much better than Chapter 1, which read to me like a last-minute collection of random stuff designed to get the PC's to 5th level as quickly as possible. The story has flowed well, and although my players didn't always know what was really going on, it all made sense eventually and we've had lots of fun through the twists and turns and it's kept me on my toes too helping to create a 'living thing' out of pretty static adventures with a lack of coherent back-story.
From here, we re-join the 'plot' as written in Chapters 2+ - should be obvious to anyone who has read SKT.
Except I'll be running three different, parallel 'threads' - the two others will also start at or around 1st level, and get them to 5th level for Chapters 2+ - one will be 'Murder in Baldur's Gate' but set in Luskan, plus some custom-built stuff north of there; the other might well be Lost Mines of Phandelver. At some point, the three threads may overlap, then converge.
My thanks for the inspirations in this topic so far.