That is exactly what we suggest. Generally expanding the domain in space so that the eye of the storm is a storm width away from the boundary works. Also, if you do not need the entire time frame that you have data for, you can constrain the times so that the storm does not approach a boundary. This is often relevant for storms in the Atlantic that curve N towards Europe for instance.
If you do expand the domain, constraining the AMR regions is the way to go. Often times I will place a region across the entire domain that restricts the refinement to to the first few levels and then place a region around the area that I am interested, allowing full refinement in these regions. The following code does this.
regions.append([1, 3, clawdata.t0, clawdata.tfinal, clawdata.lower[0], clawdata.upper[0], clawdata.lower[1], clawdata.upper[1]])
regions.append([3, 4, clawdata.t0, clawdata.tfinal, -98, -96, 25.5, 28.0])
Here the first region lets refinement occur at levels 1-3 throughout the entire domain and the second allows up to 4 and forces refinement to 3 in the region specified. You could also just change 3 -> 1 and allow the code to decide how to refine in that region.