The one thing I see missing are log backups. You don't list those as the types of backups, but you have databases in FULL recovery. If you're not running log backups, then you're probably watching your log files fill up & grow.

The general approach, working with the business to understand their recovery needs, is the right way to go. Backup and restore are not technical issues, but business ones. Just make it very clear, if you're in Simple Recovery, you can only, ever, go back to the last full or last differential. No other options are available.

As to the reporting databases, not only would I make them Simple Recovery, but I'd make them Read Only. That's a huge performance win (you'll have to swap it from Read Only as part of the load process).