First of all, there is a thing called a titanium companion cup. It is shorter and wider than a normal titanium mug, but only about 12 ounce capacity, as I recall.
If you can't solve the problem that way, you could look for an alternative stove.
I was fooling around with the same problem the other night. I also wanted to rig up a metal foil screen around the burner. I mistakenly grabbed a piece of aluminum for that, and of course it failed miserably. Then I grabbed a piece of titanium foil, and it seemed to work fine. The titanium heats up until it is red-hot, and it seems to hold a bend after that.