You're so right - matching top and bottom thread is the way to go! I won't put myself in the position of not matching the threads again.
After I wrote the request for advice, I did experiment a bit with tension, and tightened the bobbin tension and loosened the top some more. That helped - only a little bit of thread occasionally shows on top. I'm in a hurry to finish this quilt - it's a present due on March 13.