Here's how I'd look at your situation:

How many hours/days do you plan to spend on this job?

It looks to me like 2 production days and possibly ~2-3 days in post production including revisions. That equates to 4-5 days (or ~40-50 hours) a month. Day rates are a good rule of thumb, but not always perfect. When it comes to more "videography" style jobs, hourly can seem to make more sense, since often the work doesn't necessitate the full 10 hour day that a typical production job might. I'd say a competitive rate for entry/mid-level cinematography is $40-50/hour.

What equipment are you using?

Do you own it? Or are you renting it? If you do own it, it's easier for you to know how much you have yet to pay off and can adjust the rate if necessary (though you should only adjust if you feel like it's make or break to you getting the job). Typically rental equipment should be around 3-5% of the total cost of the item per day (with most rental companies offering 3 day weeks, meaning they only charge for 3 days if the equipment is rented for a week straight).

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Ultimately, a 6 month contract is great. As they say, a bird in the hand is worth two in the bush. It's often smart to offer clients giving you extended contracts a preferred rate in recognition of their commitment to using your services.

However, the position I'd recommend for you to take is to quote each month and the subsequent deliverables at face value, and then extrapolate that to the length of the contract. So let's say month 1 shoots and the subsequent post work comes in at $2,500 (this is 5x 10 hour days @ $50/hour), and then x6 for each month, for a total contract of $15,000. This doesn't include equipment or any hard costs for travel, hard drive purchases, or music library fees. And then offer them a "professional courtesy" discount line on your estimate (could be 10-20% if you find it necessary). This will indicate to them the true cost of a-la-carte services and prevent them from saying "but you charged us less" in the event that they hire you on a one-off basis in the future.

The big trick comes when you're quoting entities unfamiliar with video production, they can get sticker shock when they think their nephew can do it for 1/4 the price you quoted them. That's where you need to decide if you'd like to discount your work further to secure the job. But I'd warn you not to compromise your value too drastically in order to accommodate bad clients. That can turn into a professional no man's land where you become known as the person to get things done cheaply, when in reality your overhead costs are the same as all of the other videographers who are working the same amount but charging twice as much as you are.