The warrant is a Local Authority Warrant of Control. It is issued by the Council to the Enforcement Agents. The warrant does not have a physical or printed seal. However the LA can only issue it when it has been authorised by the TEC.
In so far as I understand the enforcement rules the bailiff has to provide you with a printed copy of the warrant if you ask for it, or a copy of the electronic record if you're happy with that. If the bailiff refuses to give you a copy then it probably means that the warrant has expired or more likely the warrant is for a different address.
Where the bailiff attempts to enforce a warrant but you don't live there, then the bailiff can seek to trace your correct current address. If this is successful then the Council needs to apply for the warrant to be re-sealed (re-aurhorised) with the new address.
By now the Council know your current address because the TEC will have informed them of the address used on your Out of Time and Witness Statement forms. You mentioned an office address, the bailiff can try and enforce there when he has an updated warrant.
As to an N244 application, the fee for a review by a district judge is £119 for a hearing on the papers only. And £303 for a hearing in person. And you won't get the fee refunded even if you get the case before the adjudicator and win. And given the complexity of your case I would only recommend the hearing in person.
You can also get advice from
Bailiff Advice Online.