As number of years a user will continue to stay with organisation grows, their mailbox size will grow as well. For an example I am with current organisation for close to 13 years and my mailbox is close to 7GB after shortcutting and emails older than 6 years are cleaned up from my mailbox by IT though.
I can share what I have seen, basically you covered the points already.
1. Inform users how large number of items in their mailbox would impact performance of Outlook.
2. Educate users to export to PST (if your organisation allows).
3. You already have shortcutting in place yet it cannot keep on bring the size of mailbox down if number of items in mailbox continue to grow (like my mailbox).
4. Inform users couple of months beforehand that emails other than __ years will be deleted from their mailbox. You may have to send reminders few times.
5. Finally if you see mailboxes still large then as you mentioned run delete activity to get rid of old email as per your business policy requirements and suggest users to use search site.