there are two ways to make the pits smaller one is to increase the number of tiles in your Material tag but to avoid seams you should stay with even numbered tiles or to increase the number of dots in the image. Or you can double the size of the canvas in the original image then copied the image layer 3 times and arrange the layers to make a seamless image at double the size.
Then do a Polar to Rectangular on that.

all of that works on the upper dome since it’s a hemisphere and basically it’s the “Mercator projection” type of distortion (from earth global maps) that you need. On the lower body of the barbeque it would be a lot simpler since it’s really close to a cylinder so cylindrical projection with the image without Polar to Rectangular would work fairly well.