We could set our customs tariff at whatever we want it to be. At the moment it's high because the EU is protectionist. But we would have the freedom to lower it to stimulate RoW trade, or rise it to protect our domestic producers - it's the flexibility to be dynamic.
There does seem cross party (Con-Lab) support for the white paper proposals. The only thing Labour wanted different were unilateral EU status (that will be sorted bilaterally soon anyway) and protection for workers' rights (carrying across EU standards into EU law, rather than becoming Singapore; which I think the Tories are fine with, but want to retain the threat of the alternative).
Soft Brexit would be disastrous because 100% of voters would be unhappy. There'd be no return of sovereignty or end of FoM for the leavers, and the EU would dictate rules to us, which would go in a much more German corporatism or French statism direction without the UK's economic liberalism counterbalance. I.e. losing our influence to direct it would make it increasingly unattractive for British interests. It's the worst of both worlds.
The FTA route would get the 52% on board straight away, and the improving economic position as we re-engage the world would slowly win round the rest.
I don't think parliament will be too much of a problem. The Tories will whip their c.25 soft Brexiteers (apart from Clarke) reminding them that the alternative is an election, while the Labour leadership will be deliberately ineffective again so they can appease both their ex-UKIPs and students, while also getting what they ideologically want (an end to big business undercutting British workers through FoM).
