The Elder book has a line in it about going ahead in absentia if a person "repeatedly" fails to show for a J/C. My money is on the fact they will not go ahead until the second time so that they have their backsides covered on the "repeatedly" point should you appeal on that point.
As has been mentioned, the elders would have initially had two of the body "investigate" - i.e. get their ducks in a row as in having two witnesses.
Now you say one witness is "anonymous" - did the elders tell you that or your mother. If your mother said it then you can give it what credence you wish. If the elders said it then that is unusual because you can demand to know who the two witnesses are.
Maybe they have camped outside your house to get "evidence". If so then they have all they need.
A letter denying "any judicial wrongdoing" and demanding to know the sources of any witness against you, copied to your branch office might get them off your back if they don't have two witnesses who will stand up and say they know/heard you admit that you have been having an intimate relationship.
I think you will be DFd soon because it appears they believe they have all they need to do so.