Lids are a useful thing. So are pot grabbers. Here's a 2-in1 solution.
Out of a silicone baking sheet, I traced the circumference of my titanium cup, which doubles as my pot.
I cut it out, poked a small bit of Triptease through it, and sealed the hole with a bit of GE Silicone II. I did that to help prevent the hole from ripping open.
With my stove, I've tested this a half-dozen times. Here are my findings:
1. Silicone can withstand some heat, but not direct flame. I make no guarantee this will work well for your stove, but I had no problems with the silicone melting or catching on fire. The Gram Weenie stove I'm using was designed to minimize flare-ups around the mug, so there is little worry of lid failure due to heat.
2. After the water came to a boil, I lifted the lid off and used it to grip the handles. This thin sheet of silicone can get hot, but will cool relatively quickly once off the pot (10-20 seconds), and works quite well to grip the small handles of my mug.