Thank you for taking the time to read and respond to my inquiry. I have tried the various bit rates, and the rumble is present to varying degrees. It's really a puzzle. As mentioned before, the problem is not present when exporting into a different format, such as .wav. Currently, I have to export as .wav, then open the file in Sony Vegas and re-export as mp3 (mono, 128kbps), and everything sounds clean as a whistle.
If I could ".wav" a magic wand, I'd want to see Studio One using the exact same mp3 codec with the exact same options as found in Sony Vegas.
Again, thank you so much for your thoughtful reply.