What I'm going to recommend won't help uncurl an already-curled scarf. HOWEVER.....
I was telling someone in the chat room last night about tubular knitting. It's similar to Amy's double knitting video, but you only use one strand of yarn. Here's how it works, in case you don't know:
You cast on an even number of stitches, about twice as many as you think you need for the width.
Row 1: K1, sl 1 wyib as if to purl to the end
Row 2: K the sl stitches, sl the K stitches.
Repeat row 2 till it's done, whatever length you want. This will be closed on the bottom and sides, but is a double-sided fabric that is thick and cushy, is showing stockinette on both sides, and will not curl.
If this is a scarf, you end up with a double-thickness, non-curling thing without any of that darned sewing. It's wonderful!
I am imagining making bags, hats, scarves, etc. with this technique. It's thick and squishy like double knitting, but without the hassle of the two balls of yarn.