We struggle with white rot on our allotment and have yet to find an area that isn't affected to some degree.
Very dry conditions in April helped in holding it back this year but eventually the garlic started to show signs so it was a case of lift it or lose it. In the end 20% of the crop was affected which for us is quite low and leaves us with 138 bulbs of various sizes. Sounds a lot but taking into account small bulbs and cloves for next years seed it should be about right.
As an experiment one bed was split into three bands with compost mulch in the centre and wood chip at the ends. I can't say there was any noticeable differences in the crop.