"If the flame is too wide , than it is too wide."
Why didn't I think of that?
I have one or two tiny burners that make flame patterns that are too wide for certain mugs and cook pots. So, I got out my titanium foil scraps and put some together into one strip that is 0.75 inch wide and about 11 inches long. Then I curled the strip around and made interlocking tabs on the ends. That made a circular strip or ring, and I cut some notches in it so that it sits on the three pot supports of one of the tiny burners. In effect, it makes a flame containment ring, and the mug sits on top of the ring. It weighs just a few grams. After a minute of use, the ring gets orange hot, but that does not bother the titanium.