It's false because the EU has decided not to do the Pick Me dance
OK so all EU politicians tell the gods honest truth and all UK politicians are lying. Ok you win, I give up. 
We quite patently would have more information
Not quite so obvious to me. I have heard many times that we will decide when the UK has decided whether its leaving or not. If we had another referendum I can see the EU leaving the real negotiations until we have really really decided if we are leaving.
will substantial sums of additional money be going into the NHS
Again we wont be able to know this until after the second real negotiations take place and we really really leave the UK.
will we have an immigration policy that matches that outlined in the referendum campaign
Again we wont be able to know this until after the second real negotiations take place and we really really leave the UK.
So its just a rerun of the first referendum, whats the point? Would there be a best of three? And if not why not?
So still no answer to incentivising the bad deal conundrum, except now the EU aren't doing a dance, apparently! 
in the unlikely event of a second referendum, what would the EU need to do to secure your vote to remain? What's your price?
I want to either be fully in or fully out. I hate this division of being half in and holding the EU back. If we had the option of fully leave or fully stay, the Euro, Schengen, the whole shebang and the country supported it, then I would be on board.