Personally I think the only way that something of this magnitude could ever be done is gradually.
Sounds good in theory, but impossible in practice and the voters wouldn't trust Parliament either.
After all, the public never voted to join the EU. We voted to join a trading union, the EEC, which was (and still is) perfectly sensible, to make cross border trade quicker, easier and cheaper. If we could go back to that, I'd expect the vast majority of the public would accept it.
But, over the decades, our politicians signed us into other closer integrations, such as freedom of movement, closer integration of tax, european courts, etc., all of which are now inherently embedded into the trade agreement. Eg, we have harmonised VAT rules, etc which mean you can't go back to free trade without also agreeing to keep the cross-border VAT rules, so that brings common tax policy back into play, and so it goes on.
It's like a divorce. Of course, in a perfect world, when you divorce it would be all fair and amicable and I'm sure most people hope and work towards that. But during the process, cracks appear, and before you know it, you're at each other's throats. That's why a "soft" longer term brexit would never work.
Personally, I wouldn't trust the politicians to carry it through either - if we just withdraw slightly to appease the brexiteers, I believe the politicians would stealthily continue with ever closer integration. As has been proved, we couldn't trust them to "brexit", so I'd never trust them in some kind of longer run "one foot in, one foot out" approach.