Well, I'm making some headway, but it's still failing.
At this point, I realized that there is also an msi in the Build folder, so I changed my script to say:
start /wait msiexec.msi /i "Build\[myPackageName.msi]" /qn
and the install process stops after about 30 seconds with no errors (return code 0). When I run it without the /qn switch, I can see that it's quitting after the dialog displays "Gathering required information...". I'm still not getting any log files.