A paper or light cloth towel suffices in place of a lid in every circumstance I've run across. Barring almost ready to eat meals in plastic containers designed for microwaving (which I use exceedingly rarely), plastic never enters my microwave.
I typically put a plate on top. Wouldn't trust paper or cloth to not ignite in the microwave?! At least my gf thinks I'm crazy to put things in the microwave that contain cloth or paper at all, and I don't know that it's safe for more than a few seconds. Food that I store in the freezer in glass containers typically needs heating for at least five minutes, usually more depending on amount
I can verify that paper towels will not combust after multiple minutes in the microwave. I usually dampen a (clean) hand towel to wrap/steam tortillas (under 40 seconds) and have never had an issue with that either.
I'm not sure that a dry cloth has enough microwave cross section (for lack of the proper term) to heat significantly, and a damp cloth therefore wouldn't go above boiling point. I'll experiment in my cheap office microwave.
Why do you think a paper towel would ignite? This has never been an issue for me. I use a paper towel which often times I can use for my hands or mouth after eating.
I'm doing it as well because I though it would be fine (I was mostly wary of BPA leaking from the plastic to my food so it didn't seem too big of a problem to microwave it), but that's a habit that you can change if you know about the risk. (And manufacturers should be mandated to engrave a warning in the lid “do not microwave” so that people are &actually made aware of it).