It doesn't matter what the "wider public" believes fifty plus years after the fact. Most don't care who assassinated JFK. Very few could tell you even the most basic facts much less the pedantic details that are agonized over in forums like this one. People believe lots of things that are not true. Polls often show that a majority of people believe in UFOs, ghosts, Bigfoot etc. It's more fun to believe in these things or at least profess a belief than not. Harder to prove the negative with certainty. How many cable TV shows are there about ghosts? If they went ghost hunting every week and never found a ghost, the show wouldn't last very long. The basic evidence in this case is solid. The implications of the alternative narratives are wildly implausible even if there were any credible evidence of a conspiracy. Many people will just never be convinced by any amount of evidence. They need or want a conspiracy. It doesn't matter because those beliefs don't change the facts. Either Oswald pulled the trigger or he did not. The historical truth of which fact is correct is not impacted by how many people believe in one or the other. All the more so when most people expressing an opinion have very little knowledge of the actual evidence.
I believe you will find it is the minority who believe in big foot, flat earth, UFOs (although by definition they are unidentified, I suspect you mean visitors from another world), Bermuda Triangle, fake moon landing etc. Oh and also in that category would be those that believe Oswald acted alone. But don’t let the facts get in the way of your story.