Thank you, that paper contained the solution. The trick is to consider r^2=x'^2+y'^2 as the variable of interest, and note that it may be measured negative; then construct the confidence bands using the ordering principle given in their section III, with a numerical rather than analytical calculation of the likelihood ratios since the probability depends on x'^2 and y' in a complicated way rather than straightforwardly on the distance from zero. But that's all implementation details, the concept is exactly what Feldman and Cousins outline.