Every time I've done the Minigaig it's been from South to North, making a loop out of Feshie and Tilt.
I've always varied from the traditional route, going on the advice of theflyingpaddy, a fellow paddy retired from this forum. Instead of carrying on to the woods on the north shore of the Allt na Cuilce, follow the ridge to the 912m trig point east of Leathad an Taobhain, and then get to the landy track on Meall an Uillt Chreagaich.
A bit of portage, but five years ago (when I was last there) it was preferable to the more westerly route. That's how I link the Minigaig and Feshie.