Don't hold the backup queue lock across a backup operation

This got lost in the shuffle when the backup process was retooled to run
synchronously within a single spun-off HandlerThread.  Formerly it was okay
to hold the lock around the point in time when the backup service thread was
being spun off, but once that became synchronous it wound up locking out
apps' calls to dataChanged(), which in turn led to ANRs.

Bug: 2421333
Change-Id: Icf378e5733af5f28a689c564494486cd3555eca7