Advice time please!

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So, I'm knitting a scarf for my Aunt for her birthday--just a basic 6-stitch cable up the middle, surrounded by reverse stockinette, and a 4-stitch border of garter stitch. The garter stitch border is, of course, there to keep it from rolling, in theory.

Here's the problem: it's now "rolling/folding" at the edge where the border meets the rest of the scarf! I've never had this problem before, and I don't know what to do about it--I've tried knitting tighter at the transition from border to middle, I've tried knitting looser, I've tried blocking it to get it to stay flat, and nothing works.

The scarf is now 3/4 done and I don't have time to redo it (plus I really like the way it looks when I flatten it out!) so I'm trying to think of something I could put on the back to keep it flat--my boyfriend suggested that I sew fleece to the back to make a super warm scarf, and I think that would work but might make it too bulky. If I can't think of anything else, I'll try that, but I figured I'd check with you lovely crafty ladies and see if anyone has a better suggestion!