I have doubts about pushing it back on his property beffore he has agreed to it, but this is just crazy. It's his car, and you are recommending the OP snatch it. They will always be enemies if he does this.
He can claim all he wants, but it's not abandoned. His neighbor believes that it is on his property, and iiuc, half of it is.
The neigbhor doesn't know that. So it doesn't matter.
It might matter with regard to adverse possession, but I don't think there is much chance that the nbor has gained adverse possession. There are a lot of requirements, and the OP should see the entire florida statute, plus all the case decisions that follow from it. If there is a public law library, or the book is at the public library, he should read the Florida Annotated Code, but even there, he'll only find a tiny summary of each case decision, and it may be hard to read in the strange language they sometimes use.
Nexus/Lexis has case law, but it's hard to find that for free.
The hard part is convincing the neighbor. I don't know how much surveys cost or if the neighbor will want a full survey or only a surveyor to review the OP's survey. Rather than or in addition to the dinners, the OP might agree to pay for half of the neighbor's expense on this. Of course he's not entitled to that, but the goal is to be on good terms with someone he might spend 40 years living next to.
The OP may wish to aks on misc.legal.moderated and for more general info on adverse possession IMO, groups google this ng in the past two weeks on the word "eunuch".