Background updates from internal server not working as expected

We're experiencing difficulty with deploying Flash Player updates from an internal server. Using Active Directory Group Policy software installation, we deployed 18.0.0.241 (Extended Support Release) using the Windows Installer (.msi) packages for ActiveX and NPAPI. We also deployed mms.cfg (UTF-8 with byte order mark) containing (potentially-sensitive info altered to protect the not-so-innocent):

AutoUpdateDisable=0

SilentAutoUpdateEnable=1

SilentAutoUpdateServerDomain=updateserver.corpname.tld

SilentAutoUpdateVerboseLogging=1

I downloaded the background updates cab file for 18.0.0.255 (Extended Support Release) and expanded the files to the appropriate path on the "updateserver.corpname.tld" web server. As expected, I can access http(s)://updateserver.corpname.tld/pub/flashplayer/update/current/sau/currentmajor.xml. The web server certificate is supplied by Active Directory Certificate Services and is trusted by all domain-joined workstations. When the update task runs (on schedule or by manually triggering in Scheduled Tasks), these entries appear in FlashInstall.log:

2015-11-2+21-11-24.766 [info] 1628 updateserver.corpname.tld

2015-11-2+21-11-24.815 [info] 1629 updateserver.corpname.tld

2015-11-2+21-11-24.826 [info] 1614

2015-11-2+21-11-24.828 [info] 1615

2015-11-2+21-11-24.829 [info] 1618

2015-11-2+21-11-24.832 [info] 1619 1063

2015-11-2+21-11-24.852 [info] 1628 updateserver.corpname.tld

2015-11-2+21-11-24.853 [info] 1629 updateserver.corpname.tld

2015-11-2+21-11-24.854 [info] 1614

2015-11-2+21-11-24.855 [info] 1615

2015-11-2+21-11-24.856 [info] 1618

2015-11-2+21-11-24.858 [info] 1604

2015-11-2+21-11-24.858 [info] 1608

2015-11-2+21-11-24.867 [info] 1612

2015-11-2+21-11-24.869 [info] 1620

I see no corresponding entries in our web server access logs, so apparently the updater isn't getting that far. We aren't using a proxy and the background updates server is internal to our network.

We primarily have Windows 7 Pro (64-bit) clients.

I've checked topics with similar complaints and haven't been able to find a solution.

Ideas would be appreciated!