Can’t see an alternative.
Is there a way of those wanting to leave leaving and those wanting to remain remaining?
The reason the whole political system is deadlocked is that Brexit is a rather vague concept. In short, leaving the EU as a member is entirely different from leaving the European Economic Area, the Customs Union and Single Market. These fundamental differences made it pretty likely that we were going to need more than one referendum on Brexit. In 2015 I wrote an essay on Britain leaving the EU and one of the arguments put forward by academics and one I adopted myself was this idea of 'Neverendums' because of the distinction of leaving the EU and things like the EEA, CU and Single Market (also other things like Scottish Independence but this is irrelevant right now).
In hindsight, the real failing of this Brexit process is the lack of consensus between the major parties and the single person I would blame is Theresa May as she only really engaged the opposition to her deal at the 11th hour. Her strategy was to essentially blackmail the likes of Boris Johnson, Ken Clarke and the ERG with 'no deal' (for the Remainers in her party) and 'no Brexit' (for the Brexiteers). In fairness to her, it doesn't help that a lot of Brexiteers have hardened their stances or moved the goalposts on this as well. For example, the 'Norwegian model' was used by the likes of Nigel Farage as an example for Britain to follow (and frankly, not the end of the world) to then pushing for a harder 'no deal'.
Whether you support it or not, the best way to go about things now is to hold another GE and/or referendum on Brexit as nothing else is going to break this constitutional crisis we have.