I actually had some of my most enjoyable dates with women I met on Craigslist personals -- where half the time, they didn't even share a photo. I just went by what they wrote and how they wrote it, to determine if they seemed intelligent, relatively honest, and if we had some things in common.
I gave up looking for "ideal" profiles (same interests etc) because I found that the more "ideal" they sounded the less likely they were to respond. As you said
When I put in the effort to really read through detailed profiles, compare "compatibility percentages" based on tests we both took, and contact people who shared mutual interests and beliefs.... I generally got no response at all.
In the end I did not worry if "they seemed intelligent, relatively honest" etc and I just contacted those which were (1) shorter than me (I'm a guy); (2) 0-8 years younger then me; (3) reasonably near to me ( I was in a big city anyway); and (4) not ugly in their photo if there was one. That way I met some girls from utterly different backgrounds from mine (including, believe it or not, an ex- Playboy Club Bunny Girl, but she was not as hot as that might sound) and found that whether we clicked or not was orthogonal to commonalities on paper. I never expected nor wanted an intellectual sparring partner.