Unless "lots of $$" is capable of warping time, no. Bay of Pigs was a year and a half before the Missile Crisis. I don't think the whole truth about about Bay of Pigs will ever be known, but from what I can recall, and I can't cite anything, the plan hit JFK's desk while he was very new on the job. The idea of getting rid of Castro appealed to him greatly, but he felt US fingerprints could not be seen or it would lead to a blow-up in Berlin,and one great truth about the Cold War was that we could not allow a blow-up in Berlin. CIA's plan called for a landing near Havana, where Castro was not very popular, in the hope that an indigenous uprising would occur. Kennedy decided that the team should come ashore quietly and melt into the mountains to function as guerrillas. CIA's alternative site was a rural area where Castro was very popular and where the LZ was impossible. Yes, they set him up to teach him to keep his mitts off carefully prepared plans, but the point is, with something like this you either accept it or reject it - you don't sit there and try to re-draft it off the top of your head. It's a shame they were playing so rough but these are the facts of life. He was grossly inexperienced. The biggest losers were those men on the beach.
I watched about 30 min of the film, will try to watch more tomorrow, but it is incredibly bad - represents the state of the inquiry in the late 60's. Much more is known now. Of course there was a cover-up, put in place before the assassination at the president's direction. Robert Kennedy was in charge. That's why the whole government swung behind it. No one expected JFK to be the victim. Set aside some time - lots of it - and read Ultimate Sacrifice. Read it carefully, check the notes, then read it again. I don't have time to explain it fully, and my carpel tunnel is acting up, but it is all perfectly clear. They were preparing a big surprise for Mr. Castro - probably would have worked, but very dangerous. They were flirting with World War III. Some of the "contractors" saw a way to rid themselves of their biggest nightmare and took it. Kennedy probably understood the risks, explaining his strangely-fatalistic remarks. Read the book. Just don't call he a Scotch-Irish/Copperhead.