Hello dm871,
Yes, installing a newer version of the Windows Update Client is one of the possibilities to get back to search times that can be beared (both fixes you mentioned are the Windows Update Client, even if KB3102810 doesn't name it).
WSUS Offline Update actually takes care of this and installs so-called prerequisite updates before starting the full update run. We are searching each month (or even continuously) for new prerequisites, because Microsoft scrambles the update system from patch day to patch day in a way that previous prerequisites may not be sufficient anymore.
Greetz
Gerby