The Parol Evidence rule excludes statements revealing these indications of prior oral agreement though they would be admissible in an action for rectification. When we have to choose between 2 or more meanings, we look not to actual intentions, but to the objective framework of facts, within which the contract came into existence, and to the parties presumed intention in this setting. We do not take account of actual intentions, because this would be time consuming, and prejudicial as it would give too much weight to those factors at the expense of the written contract. Evidence of intention may exceptionally be allowed, if it negates the inference to be sought from surrounding circumstances. Similarly, presumed intention should apply when the court has to decide if a term is to be implied.
Implication is merely another instance of construction.
Yes - the discussions were not negotiations from which gradually evolved the terms of a bargain. I doubt whether the fiction of making the parties reasonable and fair makes it any the less difficult. Here, the common assumption masked the need to explore what further provisions should be made. Negotiations may have led to a number of different, but reasonable solutions. Easier to see that the parties never agreed to be bound in an unexpected, but fundamentally different situation - than to say they would have agreed to continue the contract with the term implied to govern their rights and liabilities.