Sorry for the delay. Its not wise from a security point of view to have an account configured with full access to all mailboxes the previous Exchange 2003 config you had was not following best practice.
However it can be done and I know what you mean re: Out of office setups etc been there myself. I did not test these but try the following commands.
You still need to use the shell : -
To add the permission to the mailbox store: -
Add-ADPermission Identity Mailbox Store User Admin User ExtendedRights Receive-As, Send-As
This should let you open the mailboxes: -
get-mailbox -resultsize:unlimited | set-mailboxpermission -user "Admin user" -accessright Fullaccess
You will need to run the second command regularly for new mailboxes.