Hi Elijah,
I'm not aware if this has been specifically researched by anyone, but I have a few thoughts about EBK with low and varying sampling density.
For the same subset size, the area of a subset will be larger for a low-density area than a high-density area (ie, 100 points would be spread out over a larger area for lower densities). EBK assumes stationarity within each subset, so to get best results, you should configure the subset size so that the resulting subsets are small enough in area to assume each is stationarity.
EBK (when a transformation is used) and EBKRP are based on Simple Kriging, so they assume a uniform density within each subset. It's ok if the density of the samples varies globally (ie, some areas are densely sampled, and others aren't), but it's important that the density of the points be relatively consistent within each subset. Again, this may require configuring the subset size.
EBK Regression Prediction, however, has a clear advantage for low density sampling, but it's the regression part, not the EBK part. The better the regression model predicts the dependent variable on its own, the less need there is for including autocorrelation from neighbors with EBK.
Hope that's all clear,
Eric