One possibility underlying the poor kriging performance could be the field plots (location and sampling intensity) failing to capture the spatial autocorrelation (or spatial dependence) in the data.
It would be necessary to observe how well the theoretical semivariogram fitted to the data (experimental semivariogram) (Figure 1). If it is the case, one possibility is to try other type of theoretical semivariograms (it seems you used the type "spherical", but there are others: Gaussian, exponential, circular, etc).
Figure 1. Illustration of semivariogram parameters: sill, nugget and range (A). Example of experimental variogram and (theoretical) spherical semivariogram (B). Source: adapted from Sanz et al. (2012).
The best kriging method depends on the nature of the variable which is being studied and the type of auxiliary data available. For example: if the data is stationary (i.e., it has a constant mean), simple kriging (known mean) and ordinary kriging (unknown mean) are suitable options. On the other hand, if data is non-stationary, one option can be universal kriging. Those are types of univariate kriging.
An alternative approach would be the multivariate kriging (for example: co-kriging or regression kriging). Such methods use information from auxiliary data to enhance the capacity of spatial modelling. In the case of forest biomass, examples of auxiliary data (and auxiliary variable) are: satellite imagery (NDVI) and LiDAR (height percentiles).
The regression kriging technique for example, have one advantage which is to perform better predictions outside the sample (extrapolation), because part of the model will depend only on the relationship between the response variable and the auxiliary variable (i.e., it will not be entirely dependent on spatial variation of the data).
One interesting article about this topic (forest biomass and different kriging approaches) is:
Meng, Q., Cieszewski, C., & Madden, M. (2009). Large area forest inventory using Landsat ETM+: A geostatistical approach. ISPRS Journal of Photogrammetry and Remote Sensing, 64(1), 27–36. doi:10.1016/j.isprsjprs.2008.06.006
David Sanz, Santiago Castaño and Juan José Gómez-Alday (2012). GIS Applied to the Hydrogeologic Characterization – Examples for Mancha Oriental Aquifer (SE Spain), Application of Geographic Information Systems, Dr. Bhuiyan Monwar Alam (Ed.), ISBN: 978-953-51-0824-5, InTech, DOI: 10.5772/47967.