How to reduce microwave power to prevent burned popcorn?
A glass of water in the microwave will result in less microwave energy reaching the popcorn.  I use a large glass of water (8 - 12 oz.) when I'm softening butter because I want the water to absorb most of the energy.  For popcorn, you may get by with 2-4 ounces of water.

I've also found that the amount of oil makes a huge difference.  I sometimes pop popcorn in a paper lunch bag.  If I don't use any oil, I get the combination of burnt and unpopped you described.  With a teaspoon of oil added to 1/3 cup of popcorn, results are a lot better.  Perhaps you just need a little more oil to get great popcorn.