If Brexit is so important to the Tories, I don’t see what their issue is with leaving NI in the Single Market. It’s a tiny market, ~1% of the UK economy. And it’s not lost or anything stupid like that. It merely means that in a deregulated Britain a certain small subsector of goods might be barred or subject to tariffs. That’s it. The golden goose for those feckers should be the GB market which is 2.66tr not the 40b market of NI, that’s a drop in the ocean.
Single Market laws only make up about 20% of the legislation coming out of the EU. From the 23,000 EU laws currently in force, the EEA (Norway zone) has incorporated around 5,000, the rest don’t apply. That's the laws NI would have to sign up to. And all the EU 23,000 laws are still only a fraction of the total body of laws for a country like the UK. In no way is it like it's surrendering control of NI to EU like some right-wing, chest-thumpers proclaim. It's redonkulous.
Ultimately the decision should be NI's to take.