“…exporters from outside the EU face different levels of market access in individual EU countries.”
Do they? Why would an exporter in, say, the USA, trade on worse terms to sell his goods to France than he would to Germany. All he has to do is move his goods to Germany and then shift them to France. Like people, once the goods are in the EU (and especially in the Schengen Area) they are in and they can be shifted wherever the owner likes (unless they are goods subject to different excise duties such as tobacco or alcohol).
The issue with this very lengthy (and very complex) topic is straightforward: There are currently no restrictions (near enough) on trade between the UK and the rest of the EU. After we have left the choice is to trade under WTO (or more specifically EU "no agreement") rules or trade under some sort of bespoke agreement that some countries have with the EU. At present the EU seems to be imposing ridiculous terms on the UK to facilitate such an agreement. No other country with which it has agreements are compelled to have free movement of people between themselves and EU countries; none are subject to ECJ arbitration generally; few other countries are part of its Customs Union (though goods are moved with little friction into and out of the EU); no other countries are subject to the EU’s environmental and employment laws as a condition to do trade. There are many conditions which the EU is suggesting must apply to a UK:EU deal which it knows would be simply rejected out of hand by any other party. It’s simply trying it on to continue with its protectionism for its members and dislikes the idea that the UK should gain any sort of competitive advantage by leaving.
The EU has comprehensive general and product specific import specifications which are applicable to all importers – whether an agreement exists or not. UK Businesses already comply with those specifications as members of the Single Market so there will be no difficulties continuing to meet them. The specifications also include tariffs for use where no tariff free arrangement exists. The UK’s best option if such ridiculous intransigence persists is to walk away and export to the EU under those conditions until common sense breaks out (which could take some time).