Brexit Solution

It has become glaringly obvious that a parliamentary majority for any Brexit outcome is impossible to achieve.  I would like to propose a possible way out of the current Brexit dilemma. Parliament should have a leadership style election with the candidates being all VIABLE Brexit options. I would suggest that remain should not be an option as, while I voted that way, the majority voted to leave the EU. Also, the current Labour party option, if I understand it, is also not  such an option as, while it may be the best one, the EU would never endorse it. When the options have been whittled down to two, then a referendum  should be held with only these on the ballot paper. This would make MPs vote for what they are for as opposed to what they are against, which was the case in the previous 'indicative votes'. Also,it should mean that parties need not split, the electorate has, at least, some choice of which version of Brexit they prefer, and uphold the result of the previous referendum.