It seems like the Corona UVW Randomizer Texmap requires that greyscale bump maps passed into the Corona Normal Texmap as additional bump data, must also be passed into a Corona UVW Randomizer Texmap to generate correct tiling for the additional bump map.
I assumed that would not be necessary, but without also passing the greyscale bitmap into a UVWR, artifacts appear.
In this example, the 'WAVES' bitmap is assigned to the second UV channel and the 'NORMAL' bitmap is assigned to the first UV channel.
I feel like the UVWR is often more trouble than its worth - there seem to be a lot of 'gotchas' in terms of normal blending, integrating falloff maps, secondary UV channels, etc. Invariably I'm left with the appearance of a grid of tiles blended with some radius; the actual blending paradigm hides the seams, but produces other artifacts instead.