One of my first summer jobs back when I was 16 was working with a carpet layer. They hate concrete. Wait a minute... no that was me. I had to fight to get the gripper board nailed to the concrete floors. Sometimes they had to be contact cemented. If the nosing didn't go right across, there would be an awkward corner as they tried to transition from the nose to the "straight down". Where will the carpet end? Under the nosing or does it extend down to the next step and beyond?
Your sketch "B" was my first idea. It would normally only extend out 1" and be 1" high, basically like a half dowel (found in the moulding department as a "Bull Nose"). You want to put LED's under it, so extend it out to what you need and increase the height a bit to make it more stable. But it should be the same projection as the lower step. Make it out of 1 1/2" material and run a 3/4"round-over bit over top and bottom, to make your own bull nose with more width. Your "A" would actually act like a lever and split the plywood with time (...couple of weeks, I hear one of the patrons is a pretty big guy!). It would be stronger to apply the nose to the front face of the ply with glue and screws. It wouldn't hurt to use some glue to hold the plywood to the concrete as well as the screws.
The carpet could get attached in one of two styles. Tucked under the nose and tacked and cut with a separate piece applied on the riser, glued if on concrete or tacked if plywood, which extends down the riser and across the next step and repeats the process over the next nosing. This makes the cleanest, tightest fit around the nose. An alternative method is to simply tack the carpet under the nose and bend it down the riser and on... This is not as tight under the nose and gets mooshier the thicker (and therefore stiffer) the carpet is. These are two variations on the first style. If he uses gripper board at the bottom, the plywood would keep you from being the subject of a voodoo doll or the like. If you used Sapele as the riser, you could stop the carpet under the nose. But then the lower step would need a Sapele riser...
The second style is to let the carpet come off the nose, and "cascade", pulled tight down to the next tread and tacked in the corner of the tread and riser (preferably with gripper board). This is difficult if you don't have the thickness of the ply because the staples will be trying to hold on the edge of the tread where it hits the concrete. And not well. and usually they would want to throw a few staples into the bottom of the riser. You can't use this style because the bottom step has an outside corner that would be a problem.
The 13" tread is not actually a step but a filler under the back slope of the chair back to put the outlets in...yes? Does it matter if it is 3/4" narrower? I guess it would be 3/4" plus the nose...
15 months is very good. Concrete should reach 95% of rated strength in 28 days. I'm still babying mine after 2 years...I've got plastic down in the area that I am staining balusters right now. I currently plan to green glue plywood down over the concrete floors.
Ha! You think this free?
I'll let you and a few others know when I get going on mine and I'll be whimpering for advice on the complicated stuff like acoustical/optical layout and design and your experience on what seems to works and what doesn't.
Yes, I have the shell, 16' x 26' x 11' stepping to 9' (makes a great shop since I ran out of room in my garage!), but I don't have a snappy name. And how can I start without a theater name? So you are safe for now!
(oh yes, and the spousal unit said I had to go make some more money before I can start...
We've just "finished" an addition with "my" dream kitchen (OK, guess who does the cooking). So, I've been working mostly at home for three years now. Yup it's time!