After many, many tries, I was able to get 4 good enough runs to get me a star.
I strung together 3 first places finishes, and a third place finish. I fell down once in Bowser's castle (Got knocked out in mid-air by a heavy weight) and squeaked by a surprisingly agile Toad at Rainbow Road. It was just enough for a one star rating!
The winning combo? Mii/Mach Bike. I attribute that little extra weight didn't get me knocked around. Other combos attempted was Funky/Flame Runner, Daisy Mach Bike, Rosalina/Flame Runner, Baby Daisy/Bullet Bike. I just put the Mii as kind of $#!$ it, what else can happen, and yet it worked.
With that taking up the last week or so, now I impatiently wait for The Conduit...