Holy shit. I NEVER in a million years would have guessed that having the Output Image Processing set to "TV Mode" was what was causing the problem. I turned it to "None" and the problem went away completely.
This issue is resolved...except that I like TV Mode...oh well.
EDIT 1: Further info.
There were still traces of sound popping until I disabled the "Hi Resolution Support" and "Blend Hi Res Images" options as well. If I had to make a caveman-like guess, I'd say the Hi Res engine is bumping up against the sound emulation...
This is in the Win32 version of the program, mind you.
EDIT 2: Even further info.
After switching the Output Method to OpenGL (which I can now do with no video problems, due to replacing my graphics card
), the Output Image Processing and Hi Res options can be re-enabled with no further sound issues.