I think that any recent experiments in the world can only be responsible for human-titan hybrids. There is still the much larger question of where the titans originated from and how it all started.
- We know that the titans have been around for MORE than 100 years. Exactly how long seems to be kinda vague.
- About 100 years ago, the 3 major walls were completed. We now know that these walls were constructed by a chain of titans who then used their hardening ability to seal themselves in.
- The church knows exactly how and why this was done, and are willing to protect the secret with their lives. They feel it is more important than anything else.
- Only with the start of the manga did human-titan hybrids start appearing. I think we can safely say that Eren's dad is behind the science which allows for that, and it's likely related to his research on the world and titans at large, which might or might not include the origin of the walls, the secret of the church, and the true nature of the titans. All this "truth" is supposedly hidden in the basement.
I think that the "titans" themselves might be a foil in the story too. They're not really the true enemy, other than the natural threat they have because they're mindless and they eat humans. The story really seems to be more about "us" against "them" on a more human scale. The humans behind the walls represent a sort of forced unity of people who are clustered together under a common rule using the guise of protection. Their fear of the world outside the walls force them to adapt to living under a common flag.
There are hints that there are actually many different cultures of people who lived independently, only to find their territory and beliefs being subjugated because of the "threat" of the titans. The only reason this works is because people truly believe that there is no human life beyond the walls. But now we know that there is. There is intelligent human life out there, living among the titans somehow, and they retain their humanity. That alone is a huge threat to the entire worldview within the walls.
So what do these people really want? Why are they sending their people to spy within the walls and to make themselves enemies of all humanity? Maybe it is to free them somehow? What if the walls are not for protection, but are fences? The humans within the walls are cattle maybe? Forced into the barn created by titans, allowed to breed and multiply for a century, before they are harvested for a feast? Maybe the human-titans are trying to save them by causing enough disruption to create a change, even if it costs so many lives?