The second referendum featured a Leave campaign that effectively promised, among other things, continued access to European markets on pretty much as-member ter

The second referendum featured a Leave campaign that effectively promised, among other things, continued access to European markets on pretty much as-member terms; indeed, immediately afterwards, David Davis, placed at the head of the negotiations, was promising a deal that secured "all the benefits of membership". That deal was not available, and so the result of the second referendum cannot be implemented. If you want to claim a democratic mandate for the departure options that are available (May's deal, leaving you tied to the EU on disadvantageous terms, or no deal, and immediate, massive disruptions in cross-border commerce), you'll need another vote.