Really?
The time required for a log backup is a function of the size of the backup catalog file?
The first thing that comes to my mind here is "Why would that be the case?".
The log backup history file, just as the other log files, is an append only file. We always write to the end of it.
So, the actual size of the file surely shouldn't matter.
Anyhow - I did not mean to discourage you from writing KBAs or anything.
Keep going!
- Lars