What is the evidence this occurred? One source? What is the evidence the supposed message from Connally was delivered? What is the evidence that Khomeini - who, from what I've read, made the decisions on the hostage - received the message? What is the evidence he believed it? I.e., that Reagan would give him a better deal? What is the evidence he made the decision to hold the hostages based on the offer? What is the evidence for the "better deal"? That is the quo for the quid?
Maybe the "better deal" that was promised after Reagan became President wasn't accepted by the Iranians.
If you're looking for a "smoking gun", you're never going to find one for most real conspiracies. A handshake deal doesn't leave a paper trail.
The only thing the Press can do is try to corroborate the claims that can be corroborated and it appears the NY Times did in fact corroborate at least parts of Mr. Barnes' story. I encourage you to read the whole article.
My question to you is, what incentive does Barnes have for lying about this 40 year old scandal? To me it seems like he wants to come clean before President Carter passes away. He could have come clean in the 1980s during the Iran-Contra scandal when there was more public interest. Surely he would've been offered lucrative book deals and movie deals. Instead, he waited 40 years until Carter is on his death bed.
I don't know anyone who doesn't believe there were/are conspiracies. Why do you uncritically accept them?
I'm skeptical about every conspiracy theory and do not uncritically accept 99% of them. But I keep an open-mind because sometimes there is partial truth in conspiracy theories and occasionally the theory is proven to be true.
In the case of the 1980 election, I think there's enough circumstantial evidence to conclude that a deal was made by Reagan or people associated with his campaign (with or without Reagan's knowledge). I think Barnes is
probably telling the truth due to the lack of incentives for lying about it...