There are a few notes:
Good Reason is Subjective
A good reason to you may not be a good reason for them. It could cause all kinds of confusing. So your best bet here is to really decide what you want.
Is this job more important then ______? No, well then does it really matter if they say no?
Picking a date
Now with that said, keep in mind they are looking for other candidates, but they have asked you to find an agreeable date. An agreeable date is usually close, but not set in stone. Asking to do it a couple of days later, usually doesn't even raise an eyebrow.
Hey can you do a phone interview Monday at 4pm.
No, but about about Wednesday at 3pm?
It's all part of scheduling. You don't even really need to say why your answer is no. It's ok. If your looking to postpone a more then a couple days, then a reason is customary but not required. Essentially you have all the power here.
When they come back with a date
Now what may happen is that they come back with a reason, or a timeline, that they need you to work in.
We understand that you would like the 15th, but we would like to make a decision by the 10th, and want to have the phone interviews done the week of the 1st. Is there any way you can work with us?
Now you have to decide. It's ok to say no. It may mean your less likely to get the job, but it doesn't mean that you won't get the job. They may work around you yet, or they may not have other candidates that are as strong. Heck they may even find out that everyone's answer is "need to wait" and adjust their time schedule.
Bottom line
I like seeing things in absolutes.
Is this job more important then ______? No, well then does it really matter if they say no?
Right now your trying to get some "personal time" to unwind and prep for a PHD defense. Is that time and that PHD defense more important then the job? If so then don't worry about it. Be open and honest about your needs, if you loose the job opportunity then, so what? There will be others.
Keep in mind you need to look at what your trading (Some time to prep for a critical point in your life) for what you would be getting (a chance to be considered for maybe moving to the next phase of this hiring process). Only you can decide if it's worth it. Keeping in mind that once you have your "worse case answer" your worse case is not that likely.
You're interviewing too
Also remember what a lot of people forget, you're interviewing them too. You're also in a hiring process. You're trying to decide if you want to "hire" them to pay you. Would you really want to work for a company that forced you to stress out more than needed, just to fit their outlook calendar. Sometimes the answer is yes to that, but you need to make that call as well. If they really don't care about your PHD defense and your needs for time to prep for it, then, is that someone you want to work for?
For example, I would not be willing to make scheduling accommodations for someone saying "I already have my PHD defence scheduled for that week". But I also don't care that you have or are working on a PHD. It has no value to me. I'm probably not someone that you want to work for.