I have a colleague to thank for this:
This is blisteringly fast and just works.
use Core
go
checkpoint
go
backup log “Core” with truncate_only
go
DBCC SHRINKFILE ( “Core_log” )
go
use OtherDB
go
checkpoint
go
backup log “OtherDB” with truncate_only
go
DBCC SHRINKFILE ( “OtherDB_log” )
go