The only possible way to get unfucked is to hold a second referendum
Not in a supposedly parliamentary democracy it isn't. I was against the referendum on principle and remain so. If parliament decides against deal then it is entitled and actually required to come up with an alternative. The will of the people is catchy but has no basis in law.
Sensible policy would be to press for the transitional arrangement to last as long as necesary so that all the issues can be worked out.