I found the problem. My certificate file has a DH Params section in addition to the certificate. No other tool/service has ever had a problem with this. It seems like this is a java issue as opposed to an ES issue, though.
A pem file like this one doesn't work:
-----BEGIN CERTIFICATE-----
.....
-----END CERTIFICATE-----
-----BEGIN DH PARAMETERS-----
.....
-----END DH PARAMETERS-----
This pem file does:
-----BEGIN CERTIFICATE-----
.....
-----END CERTIFICATE-----