Lovely looking tsuba Peter, I have a tsuba along the same theme.
The Takahashi No Mushimaro poem certainly seems to be the theme. I've read that the lonley cuckoo often calls in the dark of summer nights, the call is said to sound like someone calling "return home".
I realise there is no moon on your tsuba but I have also read that the Japanese cuckoo is often shown flying across the face of the moon on a rainy night. This image signifies honor and advancement in status, and refers to the story of the samurai Yorimasa defeating the Nue. As Yorimasa was being awarded, a cuckoo flew overhead calling in the night.