A general way to study the extremes of a random variable is to consider the family of its Wang distortion risk measures. This class of risk measures encompasses several popular indicators such as the classical quantile/Value-at-Risk, the Tail-Value-at-Risk and the recently introduced Conditional Tail Moments, among others. A couple of very recent studies have focused on the estimation of extreme analogues of such quantities. In this paper, we consider trimmed and winsorised versions of the empirical counterparts of extreme Wang distortion risk measures. We analyse their asymptotic properties, and we show that we can construct bias-corrected trimmed or winsorised estimators of extreme Wang distortion risk measures who appear to perform overall better than their standard empirical counterparts in practice when the underlying distribution has a very heavy right tail. We also showcase our technique on a set of real fire insurance data.