I'll have to try that.
I did pick up another explore mission for the Dilithium, and with it a Diplo mission that matched the zone to explore to try again. I set the Diplo mission as primary, and then went to the zone to scan anomalies and explore systems. After I explored the 3rd system and got my Dilithium, upon exiting the zone, I got that "Diplomatic Investigation" button, and after I aided the planet I finally successfully completed a Diplo mission.
But I like the sound of your way, I'll give that a try next. It sounds easy.