If you're doing commercial R&D, then you should focus on directed development and manage the project around the research methodology chosen. Less directed research should simply be time boxed (financially or otherwise) so that the necessary reporting deliverables are handled appropriately.
If your research is directed, it should then be decomposable into manageable chunks. Whether those chunks are on Kanban cards or not, a structured methodology inherently combats story size and scope creep.
Research is exploratory. However, good research is directed exploration. Consider some examples:
- Take ice core samples from the Arctic to test for carbon levels.
- Mapping a portion of the sea floor.
- Vaccine development for a new disease.
All of these things are experimental or exploratory in nature, but they can still be decomposed into steps, phases, tasks, and time boxes. While pure research is generally less constrained to deliver rapid results, research should still be designed to eventually yield results, even if the result is an affirmation of the null hypothesis.
While you can use Scrum or Kanban to manage R&D, I think it's likely to be the wrong approach because the business goal of R&D is neither to improve cycle times nor throughput, but to identify the success or failure of a hypothesis as rapidly as practicable.
Even in areas like pure mathematics where some problems aren't well-aligned to typical project management approaches, the researchers should have a defined methodology or plan of attack for the problem. If not, then you simply can't measure progress or deviation from a plan, which is pretty much the point of project management as a discipline.
There's Always an Artifact
Even the most esoteric, non-results driven research is expected to produce some sort of artifact within a time box. That may be a research paper, a monograph, a scholarly article, or a symposium talk. Whatever that deliverable is, that's what you manage towards.
Imagine an endowment where an academic is given a $100,000 endowment to spend a year thinking about a math problem like P versus NP. Assuming no formal methodology, the patron probably still expects regular updates on the process, or on how the money is being spent (unless it's simply a stipend). They are also likely expecting a report on the results or lack thereof at the end of the funding period.
If you truly can't manage a given set of research goals as a project, then at least manage the research as a set of artifacts and time boxes to be effectively managed. Paid research always has deliverables; you might just have to work a bit harder to identify what those deliverables are, and how best to track them.