The only thing I'm not sure I like about the plan you have is that you initialize the backup during each daily backup.

That means, if something goes wrong with the current day's backup, you have zero ability to recover from it at all.

Say, for example, that the database crashes and needs to be restored, and it happens while the nightly full backup is being done. Probability of such is low, but the whole point of backups is to make low-probability disasters less disastrous. In that case, if you don't have the prior day's full and differential backups available, your database is toast and probably can't be recovered.

Or am I misreading something?