Fixing a corrupt Log File in small downtime window
If your log file is corrupt, my concern is that a backup/restore would retain the corruption.  My approach (which would probably be faster to complete) would be:


Run a full backup.
Detach database.
Delete/rename the log file.
Attach the database and rebuild the log file.
Take a second full backup.


To attach the database and rebuild the log file, it's just additional syntax in the CREATE DATABASE statement:

CREATE DATABASE [foo]
ON (FILENAME=&lt;&lt;Path to data file&gt;&gt;)
FOR ATTACH_REBUILD_LOG;


This will force SQL Server to rebuild the log file when it attaches the database.

The risk in this is losing whatever transactions happen between the completion of the full backup and detaching the database, but it sounds like this will be a minimal risk.  If you can "freeze" Sharepoint at the beginning of the downtime window, this would help mitigate that risk.