Hmm, now that the db is in recovering status, you may not be able to (temporarily) add another log file on a different drive to allow the db to keep processing while you clean up.

Instead, see if there is another db(s) with large log file(s) that you can afford to do w/o for a few seconds/minutes while you move their log file(s) to another drive.

That is, your log drive needs free space to do work in. It's full. You can free up space on that drive by moving one (or more) of the other log files to a different drive temporarily).

That might (or might not) allow the original db to complete recovery.

If you want to try moving an existing db's log to another drive temporarily, let me know, and I can help you build a script to do it. NOTE: you should use ALTER DATABASE, NOT detach to do this.