You can not mix things together. As I understand your only option will be to use the graduate rule. When this is the case, is has no relevance when your contracts with the company ends.
When using the graduate rule you must fullfill the requirements for using the graduate rule. These are pointed out and explained here: https://a-kasser.dk/graduates/
One of them is that you must complete an education of at least 18 months (3 semesters) duration.
At what time an education is considered completed varies from different educations, but when you must complete an thesis as part of your education, this thesis must be accepted (or advance approval is ok if you can get that) before you the education is considered completed. It is the time when your University regards your PhD as completed that is crucial also regarding the A-kasse.
So if this in your case will be in April/May, I am afraid that this means you can not get unemployment benefits before April/May+3 weeks quarantine.
About the other part of your comment:
It is correct that you can go to Germany (or other EU country) one time for up to 3 months and still receive benefits from Denmark. In this period You may return to Denmark However, if you are taking a trip to Denmark, you can not be paid unemployment benefits for the days when you are in Denmark.
So the 3 months rule is meant to be used in the way that you go to another EU country and look for job. If you find job its good, and you probably will stay in the new country. If you dont find job you return to Denmark AFTER the maximum 3 months period.
After the 3 months period has expired and you want a new 3 months jobseeking period, You will need to apply again and this also requires that you have worked for a minimum of 296 hours within a total of 3 months (as full-time insured).