You know, it really strikes me as being a highly viable electoral platform to simply come out and say, "We've heard the voice of the people, but, we really can't see a way of enacting Brexit politically without causing a ton of other problems, so we aren't planning on acting on it for now because the time isn't right".
I think that simply recognizing the result as a legitimate protest vote, would be more than enough to shift public perception favorably. Discourse simply needs to be shifted from an ideological/emotional to a pragmatic centre. For example, building on a tentpole of the practical difficulty in justifying the preservation of the union of the UK whilst simultaneously separating from the EU is a very real political conundrum.