Thanks for all the advice, people! I'll give the starch a try and see what that might do.
Fireworkslover, thank you. My little border fabric is indeed a Kaufman, from the Imperial Collections, but an older one and no longer shown on their site. The shop I bought it from no longer has it in the right colorway. I've chased Imp Collections around the internet and haven't been able to find this one. Ah well - it's from my first cautious forays into fabric buying when I would just get FQ. I tend to buy by the yard or two now...
It's ok. I have so many other things to try. Maybe I'm just not meant to do a third OBW just yet!