I agree with Vat that heavily starching the fabric is probably your best bet. Pinking does help, but it's not a complete deterrent to fraying.
Unfortunately, I've found that the handling involved in trimming, trimming, trimming those straggly threads actually just makes the fabric unravel more. Unless they are really getting caught up in my seams or are getting knotted in my machine or something, I try to just leave them be & then do one trim immediately before layering my quilt sandwich. Hard to ignore them, but it seems to help.