I enjoy football... not a fanatic, but I watch it if I like a particular team. I'm a Seahawks fan by default, but I have always loved Dallas... it's a Texas thing. lol
Anywhoooo.... The problem with creating a wider tread is that you would be using 2x12s to create a standard stringer, and getting boards over 12inchs is more problematic unless you live somewhere that has a decent lumber yard. If you do it, be choosey, boards that wide can have a tendancy to be warped in the worst way. I've had to go through dozens of boards to find a few which were not not warped in some fashion. Sadly there is no easy way to get wider shelves with a stringer as the foundation. Kiln dried wood is sometimes straighter because they get the moisture out of it so quickly.
The truth of the matter is that you'll need to get your hands on various lumber, a skill saw, drills etc anyway... so you'd be better off in the long run to just build a regular bench than you would to use the stringers, if you need something wider than 10 inches.
Believe me anything which requires complex math and geometry is more challenging that building a straight forward bench. You'd likely be surprised at how easy it would come together. Stringers and rafters are among the hardest things to lay out in construction... it's the geometry of it that gets you... Measure twice, cut once.
But as I sit here and think of it, there would be a way to make at least the top and bottom "shelf" wider by a few inches, but it would require making something of a cantilever attached to the stringer. It would extend the shelf width. It would be fairly simple actually.
I'm off to bed... nighty night my friends...
La belle cose prendono tempo... (Beautiful things take time...)