Having read through this, if it were me, I think what I would describe the situation with the Express Entry profile, the visitor visa, etc., is that you were exploring all of your options for how to come to Canada, or something to that effect. You don't need to go into extensive detail about each aspect of it (with the exception of possibly the rejected visitor visa), but I'd say that as long as you're honest about the fact you were actively looking at ways to come to Canada, that's good enough.
My concern about not mentioning it at all is that they would actually be able to see the fact that you had tried. They would be able to see when you had tried. They would be able to look at your relationship timeline and see where that fit in. If you mention it briefly and it fits in with that, then you'll probably satisfy them that you're being honest. That doesn't mean they may not ask for more information down the line, and it doesn't mean that you wouldn't perhaps be scrutinized more closely. But I think you can mention it without getting into explicit detail about it. That shows them you aren't trying to hide the fact that you tried to come to Canada through other methods. Because I wouldn't bank on them not being able to see it.
I think what I tried to balance, with my own application, was providing enough information to be honest, but not providing so much information that if there was something I thought might be a problem, that I wouldn't have more information to provide them if they decided they wanted more proof or information about it. You should generally leave yourself enough room in terms of what you provide so that when or if they ask for more proof, you have not exhausted all your options for providing it and are left wondering what to do. In my case, my daughter has no father listed on the birth certificate. I was unsure how they handled that, and there's never been a father in the picture. My state laws say that I have sole custody, and I have my own story for why there's no one else on the birth certificate. But for the application I simply submitted the birth certificate, with a brief explanation for the part where it asked about child custody information that I am the only parent listed on the birth certificate, I obtained her passport alone, and that I have had no issues crossing the border using the birth certificate as proof that I had sole custody. I didn't get into a complicated story about why there's no father listed on the birth certificate. I didn't contact a lawyer and have them write a letter stating what the law is in my state. I didn't ask family members and friends to submit affidavits stating that I had supported her alone from the time she was born. I left those options open to me if they were unsatisfied with that brief explanation, so that I'd have something to provide them down the line if they decided to pursue it further.