There would be some challenges, including a small Scrum team with a relatively larger proportion of "external consultants". Would the benefits of using Scrum on a PhD research project outweigh the challenges, or is there a better agile method?
Yes, though Kanban may be a better option for your circumstance.
I'm reminded of a great quote by Dr. Kevin Thompson, the cPrime Agile Pratice lead. He began his career in math and moved into traditional (waterfall) project management on big multi-year, multi-million programs and then, as he says, "one day I got on the wrong bus" and has been a major proponent of agile ever since. When asked if he would use Scrum to build a nuclear power plant, his reply was "No, but I'd use agile principles through out the project."
In your case, Scrum will likely not work well because it requires certain (and a minimum number of) roles, and is focused on a set delivery cadence.
Kanban applies lean manufacturing principles to any work product. Focus is on flow and work in progress. Instead of planning work to be done in a "Sprint" you just maintain a well ordered backlog of work and take whatever is at the top and work that. You keep a Work In Progress Limit on your work, so you don't have too many irons in the fire and you look at the flow of your process all the time. For example maybe your review cycle with your professor keeps getting bogged down. Look at each step to see why and maybe find your professor auto files email from you so you know you need to tell him in person that you sent him a review copy.
Here is my typical workflow:
- Pending: Work that needs to be prioritized and planned.
- To Do: Prioritized list with enough details to start work right away.
- Doing: What is the work I'm working on now.
- Waiting: Not actively doing, while waiting on someone or something.
- To Verify: I may have this to have someone check the work.
- Done: Time to celebrate.