You can see if a deferment is right for you and you would not have to make a payment but you won't be making any progress toward forgiveness or paying your loan back.
Are there any other alternatives that make sense?
Yes, you could always try an income-driven repayment.
What is a graduate fellowship deferment?
It is a deferment that if you are enrolled in an approved graduate fellowship program, which is one that provides financial support to graduate students to pursue graduate studies and research, you are eligible for the deferment.
Could I be eligible for the military service deferment?
Are you on active duty military service in connection with a war, military operation, or national emergency?
yes, I am in military service.
Then you could be eligible for the military service deferment.
Am I making progress toward forgiveness when on an deferment?