I was going to suggest big game, it is extremely limp compared to other monos. Give Sufix a shot that is real limp line as well.
I second the Big Game suggestion. Most limp mono I have tried.
Standing on the water, casting your bread
While the eyes of the idol with the iron head are glowing
Distant ships sailing into the mist
You were born with a snake in both of your fists while a hurricane was blowing
One other thing to check is are you putting too much line on the reel. We use big game as well and never have that problem as it is very soft but tuff. Have you ever tried braid with a mono leader?