I did a lot of experimentation with alcohol stoves before I switched to wood. The pressurized jet stoves look like a "real" conventional gas burner, but the bottom of a soda can stuffed with fiberglass insulation works about as well and is much easier to light. The fact that a certain cantankerous and boundless pontificator up in Maine has gone in roughly the same direction confirms my conclusion that a container with a wick will work best for most people.
Rather than try to make it simmer, I just made a second stove, also stuffed with fiberglass, and added a top that had a half inch hole in it. It burned at a perfect simmer rate. I don't remember the exact run times, but I think it was a lot longer than 15 minutes. More like half an hour I think.
You could probably make a drop on cover that would make the first stove simmer, but these stoves are so light it wasn't worth the bother. Simmer version shown here: you can use a penny throttle the flame back even further, or snuff it altogether.