Very true and good point canuck. Though, being from the Philippines and knowing a lot of applicants from there, with no divorce as an option and annulment just too costly and long, I have already come across atleast 3 people in the exact same situation who were denied PR because they were a male-female couple who IRCC did not think qualified as conjugal with the same burden as OP's girlfriend. Maybe the reason those couples got rejected was for something else, I didn't pry but I can tell this OP what one of the couples did before re-applying.
The partner in the Philippines applied as a worker in Hong Kong, lived there and got a divorce decree there. Partner from Canada flew to Hong Kong to marry her. Their second application was approved with no problems. Took them many years but they did it. So from here kanuto, it is most definitely up to you and your girlfriend what to do, this is certainly one of the hardest things to overcome since the country itself just won't let exes move on with their lives legally. People here have a lot of good advice. In the end, if you can prove that you and your girlfriend are in a marriage like conjugal relationship, there really is no harm in trying, as canuck said, IRCC should not expect anyone to risk criminal charges. Let's just hope the visa officer who will take care of your application is as reasonable as we hope him or her to be. Goodluck!