I got this working thanks to TAC. I'll summarize it here for future reference:
All of the prerequisite settings were done in eDirectory:
I also imported the certificate chain from eDirectory into the Trust List in Clearpass.
And also enabled LDAP over SSL (port 636)
Finally, what got it working was:
In the authentication source settings, under the Primary tab, the password attribute should be named as "nspmPassword" instead of “userPassword”.