I get what you're saying. It sounds sort of plausible, but I think you're not right on one point, and I think your sort of thinking is why the Brexit vote backfired on the establishment. Rather than gullible, the average voting guy makes up their own mind and isn't easily swayed by propaganda. Their feelings on the EU were well-established long before the referendum, and they're still the same today. I guarantee that if we had another in/out referendum next week, the result would be the same or even more pro-Brexit. I'm pretty sure that the majority of the government don't want Brexit. Their only option now is a referendum of some sort. It'll be interesting to see what choices they put on there.
To me, there are three possible solutions to the problem. We can change our minds and remain. The implications of that on the democratic process are frightening, so it could only happen from another referendum, but that could only work if there were an overwhelming majority, which is not going to happen. Secondly, we could do a no-deal Brexit. I personally don't believe that it would be as bad as they say for the average UK guy, but there will certainly be some losers. Thirdly, the rules of engagement in the EU could change to make remaining a much better situation. With the present arrogance, that's not going to happen, but if Spain, Italy, UK and Holland all turn against the EU dinosaurs, we could see some change in the near future. In that respect, the present delay until October is going to help a lot if we can all stay calm until then. With that solution, a large majority would be happy.