I think "The plan would be that." is more natural. Which one is more natural sentence?
"That would be the plan" sounds more natural and is commonly used. This is because he is telling his audience a story about how he was supposed to write a paper versus the reality of writing that paper. "That would be the plan" is a way of reiterating the plan that you have for something. Ex: A: Are you going to go tonight? B: That would be the plan.