Is there anything in the Federal Rules or DC rules which allows
service to be in any sort of electronic means - including the Federal
Court's CM/ECF system?

To my knowledge, and from what I've found by looking, process
serving requires a witness, so most are served in person. Some
are served by registered or certified mail, but I believe the
court must specify this as acceptable. Email and other forms
of electronic communication don't offer the same degree of 
certifiability.