I give up! Can't get it working in IE, Firefox, or Chrome. The registry key is in Windows. I deleted it and let the UI patcher re-create it, and that did not help. I double-checked that the registry key was pointing to the proper path to EC PlaySound.exe. It was. All browsers are set to allow handling of the pincoui protocol by EC PlaySound.exe. I double-checked this by creating new profiles in each browser and trying the link again, to be sure I said "yes/allow" when the browsers asked. I also checked each browser's settings and all show pincoui to be handled by EC PlaySound. EC PlaySound.exe is set to everyone - full control permissions, and set to run as administrator. It appears to be running properly (as it shows up in Task Manager as using 181MB of memory, and appears to be performing other EC PlaySound features properly in-game.
Oh well! It is not meant to be, and I can't find anybody else using the feature to compare notes. Thanks for trying to help troubleshoot, Pinco!