I think JC fully understands that there is no point in a soft Brexit where we get all the disadvantages (paying through the nose, having rules dictated to us) and none of the advantages (being able to do support our own industries in whatever way we choose, being free to strike trade deals with non EU countries).
In that sense, he is honouring the referendum result, and dragging some elements of his party with him the best he can. It is not up to him to drive your liberal agenda, he has many MPs from Leave voting constituencies, like Vernon Coaker where I live in Gedling.
His best plan is to stand back and watch the Tories destroy themselves, and they are doing a fine job of that without any outside help.