Making Exim use different MX servers in a random fashion

Solution 1:

You can use the manual route to bypass the normal DNS routing that looks up MX records.

The manualroute router is so-called because it provides a way of manually routing an address according to its domain. It is mainly used when you want to route addresses to remote hosts according to your own rules, bypassing the normal DNS routing that looks up MX records. However, manualroute can also route to local transports, a facility that may be useful if you want to save messages for dial-in hosts in local files.

https://www.exim.org/exim-html-current/doc/html/spec_html/ch-the_manualroute_router.html