Fixed with this guide:
Exim with a remote SMTP server - ArchWiki
Not as simple as it looks but kinda
On the first editable block on Advanced Exim Editors, add this:
Code:
domainlist blocked_me_domains = lsearch;/etc/blockedmedomains
Obviously you'll have to put all your domains blocked on "/etc/blockedmedomains" (one per line on the file).
Then add this after the editable box right after the "# Demo Safety Router":
Code:
to_myothersmtp:
driver = manualroute
domains = +blocked_me_domains
transport = remote_smtp
route_list = * your.smtphostname.here
Obviously editting where it says: "your.smtphostname.here" and allowing to relay on that smtp (you may whitelist yourself to make it faster).