Thought I had figured it out by right clicking on the background, choosing Inspect and un-checking the box under the Styles menu next to background color. That looked great, until I realized you can't actually save changes made this way. I also tried writing it as custom CSS, including the override code (!important). That did nothing.
What finally did work was Edit Site Header>Styles>Gradient (which allows for custom editing of the background, whereas choosing Dynamic does not), then choosing 0 for the opacity value to make the main background transparent. At that point the background for my dropdown was still black. So I went back to Edit Site Header>Styles>Background and changed the color code to #000000 which seems to have worked.
You have to hold your mouth just right the whole time too.