I'm interested in applying to a Ph.D. position and the guidelines indicate that a given number of different projects (of a range of open positions) should be indicated. I'm interested in one in specific and the other options fall completely outside of my interest or even my specialty. This is required because a potential interview will include members of all the chosen projects, what approach is recommended for completing the list?
Follow the directions. If they ask for 4, give them 4. Not 1. Not 3. Not 5. 4. I don't want to hear about why you don't like the other ones. Pick the lesser of evils. The reason is that selection committees have a mass of paperwork to do and then get on to their "real job". Do not give them a simple reason for filtering you out. Not following directions shows a stubbornness or stup...err...ignorance or tactlessness or something. NOTE: I'm actually a big rogue who believes in not following rules. BUT. Not when you are submitting an application, writing a grant report, doing references for a journal publication, or submitting an EIS to EPA. You need to be gnat's ass perfect on the format and the direction following in that case.
Once you HAVE the acceptance. AND acceptances at other schools. Then (perhaps) you can negotiate, discuss, etc. But don't screw up and not get the offer first.
You need to have options. Advisors can be SOBs. Can die. Can leave and go to another school. Don't go to a school where there is only one option. There are a few cases where a big fish is at a lesser program (often money related). But you don't want to be in that pickle. Don't go to Ag State U with perfesser Fancy and nobody else when you could go to Ivy with several fancies. In fact your whole approach in the question here shows too much focus on one school. Apply to several. And this one with only one acceptable program needs to be towards the bottom of the barrel.
You will always have to work with more than one faculty member as a PhD student. Certainly during your class work, you must be prepared to interact with other faculty. During your research, you will figuratively (and perhaps literally) have to "go down the hall" and talk with another faculty on a topic that impacts your research because your advisor is not the expert on that part of the work. Finally, your dissertation committee will contain more than one faculty member.
The reason you are asked to select more than one faculty at this point is to give you the opportunity to prepare for the above situations well enough in advance. We have another reason too. Suppose that I am a faculty member who is to interview a potential PhD student for my research group. I would be far more impressed to hear the student tell me that he/she already knows about my colleagues that have potentially useful contributions to make than I will be to hear the student say "No, I had no idea that person was here".
Take the time now to get to know the place where you plan to start your life-long career. Learn to network by learning how to get to know who to contact to start your networks.
This exercise in discovery carries over ten times or more when you are later going to interview for a faculty position at a university. Do you believe the department where you will apply will be impressed when you know only about that one person in the department who has the research equipment that you need for your studies?