Your analysis has some flaws. And a company that doesn't know what job it's advertising is a mess you may want to avoid. Also, it's not common for job candidates to suggest the creation of a new job or role based on an interview, so you have risks with your approach.
Here are some concerns I would have with your approach:
Changing the title, job description and pay range should require the company to re-advertise and re-interview for the position. HR should be concerned about equal opportunity. Also these changes should attract an entirely different pool of candidates, some of which may be as qualified or better qualified than you. This eliminates one of your strongest "selling points" since they cannot rush the process.
Creating a director role may not be possible within the department or for a job that is not currently advertised as a "director". Company politics may prevent the creation of that role, or hinder it's creation while they still are in need of at least one person. And the costs are too heavy if they move too fast and make mistakes. What do you bring to the table to make a fast move worth the risk? Do you have special connections or qualifications?
You have not explained how you are best qualified for the position. First, how is it that you are qualified to take on the responsibilities? Your current salary is now below the lowest salary you recommend, in stark contrast to your original concern. Also, if the job is mis-advertised, how are you confident that a new pool of candidates will not be better qualified than you for the pay range you suggest?
In your question, there is not a clear need for a director from the perspective of the company. Has the company grown? Have the department responsibilities changed or expanded? If the company hasn't changed much then there is little basis for new roles like director. Their next step should be to reduce the job responsibilities, and place them with the EVP or another person until it is better justified, and title this role more effectively if necessary ("manager"?). In other words, how does having a director benefit the company if they were doing fine without one? It sounds like this is a new job, but maybe it should not be a director job.
As the CEO of the company talking to the EVP, I might respond to your suggestion with, "A director role will cause a lot of political chaos. Try to compromise on salary and keep the title and responsibilities 'as is'." Then there are no other VP's/EVP's counting their directors or trying to get new directors just to "keep up." Would this mean that you reject the offer? And would other candidates likewise reject it? Compromises can be effective, and it isn't clear why this wouldn't be effective but your answer doesn't seem to allow for compromises like this.
Some suggestions and alternative perspectives:
You do not explain why the job title and description don't really match what you discovered during the interview. You may want to first get a better understanding as to why this is not being advertised as a director position right now before assuming they didn't know that it was a director role. Maybe they have already explored it, maybe politics or practical reasons make them avoid it. Maybe they will reveal market research that provides a different perspective. This would help you prepare for your negotiation much better.
Also, decisions like adding a director role usually are not suggested by job candidates. So you may want to ask probing questions to get them to think of your solution instead of you suggesting it. Being proposed by an outsider may not be received well. So approaching with questions that help them realize they are advertising for the wrong job could help them understand your perspective faster or better than trying to explain it to them.
Consider that if they reject your proposition, as the CEO/EVP I would probably reject you for further consideration for the job. It would sound like your expectations are not aligned with the current state of the job/company. Hiring you after that discussion would be unwise. You should be prepared with how to address this unless you are fine with this, or else be prepared with more options.
To increase options see this as a negotiation rather than thinking up a "solution" and then trying to support/defend it. For example open the discussion with, "Can we talk about reducing the responsibilities and/or enhancing the job title? Either way, I'm concerned about the compensation level, but I think we need a discussion to clarify the expectations around the job itself first." Explain your concerns but focus on trade-offs among the job title, compensation and responsibilities. This is a more flexible conversation which may help you reach agreement.
One last option, you may want to pursue this discussion as an advisor to the company and decline the job (for now). State the reasons you outlined above regarding misaligned title, compensation and expectations. It sounds like you can help create an appropriate role and set expectations since they may not have realistic expectations for this director job. It sounds like they need help and you might want to sit out during this round of company "learning".
With this approach you will likely be seen as objective and interested in helping the company. That objectivity will probably go a long way toward making you more attractive as an employee for the company in general. After advising, you will probably also be seen as a good candidate for filling the role, but sincerely do not expect that since it is misleading. Only take this approach if you genuinely want to help, you are fine if you do not get the job and really do want to avoid what could be a terrible mess.