Please correct me if I'm wrong, but if DC is refusing to sign the paperwork, we're not going into administration anytime soon. The process takes a number of weeks according to the below and only happens at the Court stage if someone other than the owner is petitioning for it.
There is no previous example (as far as I can see) of HMRC putting a club into administration. The use the winding up petition as a way of leveraging pressure on the owner to put the club into administration.