Thanks for the fast reply.
The one snag is that the sub-networks don't show Super Admin in their dashboards -- it looks, instead, like I'm logged in as a non-super sub-domain site administrator. The Super Admin settings in the main site are set to allow large file uploads, and the sub-domains under it respect those settings, but not the sub-network sites.
I have been slowly resigning myself to the necessity (and relative ease) of relying on the MU domain mapping plugin, rather than monkeying with the database. (I'm getting really tired of issuing MySQL commands every time I want to add a new theme to the sub-network sites.) Hmm... I guess it's just my geeky pride that's standing in the way.