On the morning of 30 March, customs officers will need to have a COMPLETE schedule of what the 'new' tariffs (under WTO rules) will be. That is EVERY single item or component that arrives or departs.
Why do you think this is a problem? The tariffs are already available and Customs (or their computer system) have to deal with around 40% of our imports coming from non EU/EEA countries already. It may, possibly (probably), be an issue if (when) the new customs computer system isn't up and running on time or doesn't work properly, but otherwise that side of things is fine, understood, and there shouldn't be many problems except for end-user importers and exporters being unfamiliar with the system to start with.
LEGALLY it all has to be signed off before the truck can move. Thus even 'No deal' requires a mountain of new paperwork.
It really doesn't. It just means that we''ll be treating the 58-ish% percent of EEA imports and exports exactly the same as we treat the 42-ish% of non-EEA. Logically that's probably a 140-ish% increase in transactions for Customs to deal with (assuming we don't stop buying or selling things!) - the vast majority of which will go through without any human checking or intervention anyway.
The real extra work is for the manufacturer/exporter/importer of the goods but none of it is anything 'new' or complicated, unless you've never exported outside the EU before. And of course there are plenty of forwarders etc. around who do have the required experience, because they already do it every day.
That's not to trivialise the potential for problems with vehicles queuing at Dover/Calais but it's not potential additional paperwork that's the problem, it's just the basic physical problem of every lorry having to stop for a few minutes before leaving the port.
Obviously there will be some sort of cost implications but there's no real 'mountain' of extra paperwork to do - just an extra stage of admin processes which most people aren't familiar with.