There are a few things you have to consider.
Are you using a 3D painting program or a 2D app like Photoshop?
Will the object be subdivided?
Are you using normal maps?
Having the UVs form a closed loop means that there will not be any texture seams. However, the UV's now have a gradual distortion towards the inside of the closed loop. You can use Tangent based normal maps without worrying about visible seams. If you subdivide the UVs your texture maps shouldn't have any problems.
By having multiple UV clusters distortion will be limited, however you have to deal with seams. It might even be easier to paint on the clusters in Photoshop, instead of the 1 ring island. Painting out the seams can be challenging without the use of a 3D painting app, unless the texture is basic. Subdividing these UVs may cause the some sliding and distortion, resulting in the areas of the texture not lining up properly. If you apply a normal map, those maps using Tangent space may produce visible seams. (Materials that properly read Tangents don't have this problem) If seams are visible, you will have to use Local Space normal maps.
Hope I've helped steer you in some direction.
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