[exim] smtp auth relay for root emails only

Hello guys!

I have a server currently setup in a way that connections to a specific
group of SMTP servers are allowed only, even connection to local/localhost IP on port 25 are
blocked.
Since this setup took place I no longer receive system notifications, control panel
emails notifications, etc (which makes sense) to root.

I would like to know if I can setup some sort
of Mail Relaying for the root emails so I can receive the updates or notices if a
server issue shows up.

Someone told me that I should add a router and transport that does those
special handlings for email from root that is sourced from localhost and send it
through this specific SMTP server but I really dont know how to do this, Im a basic exim user so any help will be highly appreciated.

Thank you guys in advance!