Sir Ivan Rogers makes a good point about Norway and Switzerland

'Whatever one thinks of the Norwegian or Swiss models, to characterise Norway and Switzerland as countries which, despite their sovereign votes not to join the EU, in some way failed to make good a genuine “escape” from European political integration, is patently absurd.
'One can, by all means, argue that neither model is appropriate to the UK, and that we can do better.
'Then set out what you think is better in what you propose, and demonstrate why you have reason to think it is negotiable. With a bloc that, understandably, will think we are a much larger partner, but also a much more sizeable future competitor, than either of those, and will therefore prosecute its own interests very carefully. But one cannot argue that Norwegian/ Swiss type models are “not Brexit at all”.Sir Ivan Rogers, former British Ambassador to the European Union until he stormed off in a huge huff.'

Sir Ivan Rogers, who was British Ambassador to the European Union until he stormed off in a huge huff, speaking (at great length) the UCL European Institute three days ago. 

Sir Ivan Rogers makes a good point here. 

Neither Norway and Switzerland are in the customs union but are in practice aligned with the EU for regulatory purposes (no chlorinated chicken for the Swiss, alas). They border on the EU but the border is invisible when you cross it. So it could be in Ireland.
Norway and Switzerland are rule-takers for many purposes but it would be untrue to say that they are vassal states or that their decisions, made by referendums, not to join the EU were not honoured. They remain independent of what the EU calls 'the political pillar'. 

The Norway option (if it is still an option and that would depend on the Norwegians, Iceland and Lichtenstein admitting us into their club at this last moment and the EU agreeing) would be a good compromise solution for the UK at least temporarily. It would allow free movement of Europeans into the UK but it would not require us to give huge amounts to the EU as Norway does. Norway chooses to give the money to help poorer EU countries.

But crucially Norway is not in the customs union and for a very good reason. Being in a customs union, even temporarily, would mean the EU running our trade policy and take away any incentive the EU would have to make a trade deal with us. Third countries that made free trade deals with the EU would have accept to British markets but could refuse any trade privileges for the British in return. This is the case for Turkey, the only major country that is in the customs union and not in the E.U.

Norway does not want the UK in the EEA because the existing members meekly copy EU rules and Norway rightly thinks that the UK will not. But these objections could be overcome or a simulacrum of the EEA could be created just for the UK.

Regulatory alignment is much more important than tariffs and whatever happens British companies that export will follow European regulations, so perhaps being a rule taker in these area without any part in making the rules is a price worth paying for getting away from the political pillar. And, on this subject, please let us leave the ECHR as well.

If only we could somehow be in the EEA and somehow also in whatever NAFTA is renamed.