In my post above I forgot to mention that I think I wasn't clear in my first post. I do not keep my full backups and transaction log backups in the same file.

I have one backup file for the full and differential backup, the full backup runs with init and the diff. backup runs with noinit.

I have another file for my transaction log backups which because of my mistake was "init'ed" every time.

I obviously need to reinitalize the transaction log backup file once a day so now I'm thinking the simplest way is probably to change my full backup job to perform a transaction log backup with init before.

backup log database1 to database1logbackup with init

backup database database1 to database1backup with init

Then my 12:00pm differential backup will be appended to database1backup and the transaction log backups will be appended every 2 hours to database1logbackup until it's reinitialized by the daily full backup.