Stair riser templating when treads are already in

The answers of the tread then riser SEEM to make sense, but consider this: A properly installed tread will not come off before the lip breaks off. Using just regular Elmer's wood glue, I used to make treads by gluing the edges of 2 2x6 planks together and then planing and cutting them down (after being clamped for 24 hrs). After that, if I took a sledge to it the plank would never break at the glue joint, but somewhere else along the natural grain. So the stair tread flipping off is highly unlikely. What IS likely is that the overhang could be chipped or damaged and the tread may need to be replaced. If you go riser over tread then you will essentially lock the stairs together to where you cannot remove a single tread in the middle somewhere without tearing up a lot of the assembled stairs. Additionally, locking any wood assembly together completely isn't always good for expansion and contraction caused by potential seasonal humidity change. This isn't always a factor in certain natural climates and/or exceptionally well controlled climates, but if it can be, it should be considered.

I can't really tell what I'm seeing in your screen image, but I think your plan is reasonable. If the stringer isn't tall enough to add the individual 2x4 ledgers you describe, you could use steel angles bolted to it.

Were it my project, though, I'd be cutting the treads out and building three new stringers, using the existing setup as a pattern and adjusting for any variation in tread thickness. I'd cut them out of 2x12 or LVL stock and fasten them in place, using construction adhesive at all joints to add stiffness and prevent noise. It's not difficult and then you have a staircase built to high quality standards.