The majority are CEC candidates, since they earn more points because for their Canadian diplomas and Canadian work experience.
But, you need to breakdown yours points a little bit more. What exactly "almost maxed out" means for your language exam? Have you achieved CLB9? CLB10? Or any of your grade under CLB8 or lower? That changes everything.
Also, doing a post-graduate course (1-2-3 yrs, you choose) greatly improves your score.
I'm also 31 (so -11 points to start with), also with 3+ years of work experience, with 100% maxed IELTS (CLB 10+ in all four skills), but I do have a post-graduation certificate of 18 months, which gave me some extra points. I also got 6 points from the French proficiency test. With that, I stand at 469.
So, quick answer: No, it's not necessary to have a Masters. But you need, at least, another diploma besides your bachelor degree, and you most certainly need to get CLB10 to be competitive.