Since you are closing the relevance substitutionyou don’t need the ampersand or quotes. Try
wait {value "UninstallString" of key whose(value "DisplayName" of it as string as lowercase contains "<product name>") of keys whose(exists keys of it) of key "HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Installer\UserData\E-1-5-18\Products\" of native registry} /qn /norestart