If you do that, please take a well-lit photo of the opened-up step, and post a link back here. At this point, I'm curious what the actual internal construction of the stairs is. I still suspect what you are calling a stringer is just a trim board, and what somebody else called skirting. But if there is no center stringer, I suppose this could be a factory-made prefab staircase or something, and have dado'd stringers. You say the step feels springy in the center, at least with the detached part of the tread. If you tap the center part of the riser, does it ring hollow or solid? A tiny hole drilled in the center of the riser would tell you in seconds if there is a center stringer or not. What year was the house built? How wide are the stairs?
Also, please use your real camera for the pictures. If it is 10 megapixel, there will be a menu to turn the resolution down, or you can do it in your computer as you post it. The better lens and flash compared to a cell phone will make a much better picture.
This long-distance pro-bono consulting is frustrating at times. I'm no expert, but I know if I could see it in person, I could figure it out in a few minutes. The actual experts on here could do it even quicker. A sharp ice pick and thin putty knife, and a hammer, would quickly answer a lot of questions about what is part of what, and how it all fits together.
-- aem sends...