On the Irish Border Question

It should have become obvious over the past few days that there is no solution to the current Irish Border debate unless one side or the other backs down. The two possibilities before us - a hard border versus the same arrangements as today - are dependant on what sort of a trade deal the UK negotiates with the EU. The Irish Border question, which should be a result of the trade negotiations, has however become a precondition to them.

If, perchance, we end up, over the objections of the DUP, with a special deal for Northern Ireland, then Scotland and Wales would be quite right to demand something similar - moving the hard border off the island of Ireland and onto the island of Britain. But then wouldn't England want a special deal too, given the problems an English hard Brexit ("Engxit"?) would cause/is already causing to the English economy, and particularly to the less-well-off members of the population?

This route, if followed, would likely end up at something close to the UK (if it remained intact) remaining a member of the Customs Union and Single Market, though formally exiting EU. The UK would then, like a typical vassal state, pay into the running of the EU, but have no say (no MEPs, no representation on the Commission...) in the running thereof. It might then, with hindsight, look rather better to have remained a full member of the EU, on the terms Mr Cameron negotiated oh-so-long ago, and with influence on the EU's future direction.

The choice, if the UK remains intact, seems to come down to

            a) Hard Brexit,

            b) Vassal State, or

            c) EU Member.

Does the (Sovereign?) Parliament at Westminster have a (cross-party) majority in favour of one of these options on the most important question of our times?