When I go
Top > Service Director > Domain Manager > Name Servers > Name Servers Set Name and press
Edit I do not see all of my name servers to include in the set.
There a policy "Who can use this Name Server" set for each name server individually. It can be either "Hosting provider only" or "Hosting Service Provider and their Resellers". The name servers set you are editing belongs to a reseller account, therefore it can contain only name servers of the latter policy.
To resolve the issue please change policy for name servers you would like to include in the set from "Hosting provider only" to "Hosting Service Provider and their Resellers".