OWHM also checks the mass balance for every time step and raises a warning if its violated. The other flavors of MF-2005 only check the mass error if requested by the user in the Output Control (OC) and for the last time step of the stress period (usually the
best time step). The mass errors might be something that has been there, but you were not aware off.
You might also need to increase your solver iterations, MXITER, since OWHM considers every time the finite difference equations are formulated (FM) as an iteration, while MF-NWT only considers each time it solves for the inverse of the Jacobian. So there usually
are about 10 FM iterations for every Jacobian iteration. That is why NWT models often claim they solve in about one tenth the number of iterations compared to the other solvers (but it is really about the same number).
Last comment is that you may want to try running the model with the COMPLEX solver option. There are slight differences in the preset options for COMPLEX, MODERATE, and SIMPLE between MF-OWHM and MF-NWT, so my guess is that the later has a configuration that
works better for your model.
If you need more detailed information about OWHM specific options, check out the doc folder of the download or the published report:
Boyce, S.E., Hanson, R.T., Ferguson, I., Schmid, W., Henson, W., Reimann, T., Mehl, S.M., and Earll, M.M., 2020, One-Water Hydrologic Flow Model: A MODFLOW based conjunctive-use simulation software: U.S. Geological Survey Techniques and Methods 6–A60, 435 p.,
https://doi.org/10.3133/tm6A60
One last comment is that your zone 0 might represent flows entering or leaving the model domain via a boundary condition.