> For a variety of reasons (legal, procedural, and political) MPs can't simply resolve to reject Brexit,

There is no legal reason why ministers cannot reject Brexit; given the role of Parliament in the UK system of government, there is very little that ministers could be legally prevented from deciding, since the current (at whatever time it is you are asking the question) Parliament itself is generally the ultimate authority on what is allowed, so much so that it cannot be bound even by past Parliaments.

There are, as you note, political constraints, particularly the problem of there being no majority for any option.