Having done this type of modeling for decades, I can say that, in how your problem is defined, Kriging is a very poor choice and, without understanding nonstationarity, you are probably violating the hell out of some important assumptions. You are likely getting your stated accuracy due to overfit and not actual prediction accuracy. If you were modeling something like spread of noninvasive species (that follows a spatial die-off) you may be able to justify a model such as Kriging but not here. I would dissuade you from exploring MaxEnt because of some intractable statistical reasons see: Renner & Warton (2013); Yackulic et al., (2013); Royle et al, (2012).
As the saying goes "what is your question"? I would think that you may have a model specification issue on hand. This is where the incorrect covariates are being defined, or an incorrect hypothesis, in describing the variation in your process. My reasoning is that you are getting poor model performance in multiclass Maximum Likelihood and RF model(s) which may indicate that you do not have variables that represent variation in these classes or have very poor training data. It also sounds like you are using covariates (elevation, insolation, ...) that are indicating "potential" rather than observed (BTW, I am consistently getting after my students that elevation is not a defensible process!). By representing forest as a binomial process the variation is being reduced and the covaritaes more representative of the modeled process. I would point out that nominal variabies (eg., Natural Subregions?) can artificially partition continuous variation to the point that it is meaningless.
Potential would effectively be modeling niche, using variables that indicate environmental variation, that the vegetation could "potentially" occupy where, modeling observed would use something like active or passive remote sensing to model where the process is actually observed in the field/data. The nature of "potential" occupancy adds a layer of uncertainty that needs to be accounted for in evaluating model performance.
If you settle on modeling the potential occupied niche, then you should carefully select variables that indicate ecological process of each desired class (eg., a variable important for trees may not matter for grass). It is also plausible that your classes interact in a way that changes to probability of occurrence. An example of this would be gaps in canopy influencing occurrence of grass and forest composition influencing other understory species.
Modeling is not, and should not, be a one-size-fits-all push button endeavor. At this juncture, I highly would recommend talking with a statistician or one experienced in vegetation modeling to get some guidance.
Renner, I. W. and Warton, D. I. (2013), Equivalence of MAXENT and Poisson Point Process Models for Species Distribution Modeling in Ecology. Biometrics, 69: 274–281. doi: 10.1111/j.1541-0420.2012.01824.x
Royle, J. A., Chandler, R. B., Yackulic, C. and Nichols, J. D. (2012), Likelihood analysis of species occurrence probability from presence-only data for modelling species distributions. Methods in Ecology and Evolution, 3: 545–554. doi: 10.1111/j.2041-210X.2011.00182.x
Yackulic, C. B., Chandler, R., Zipkin, E. F., Royle, J. A., Nichols, J. D., Campbell Grant, E. H., Veran, S. (2013), Presence-only modelling using MAXENT: when can we trust the inferences?. Methods in Ecology and Evolution, 4: 236–243. doi: 10.1111/2041-210x.12004