Bruce
can you expand on what you are seeking when you say "correct" the overlaps? Do you need to change which is on top, or are you having problems where edges mismatch the underlying data?
The Mosaic Dataset is specifically designed to combine rasters, even if they are at different resolutions and projections. The Mosaic Dataset (MD) is a virtual raster - a database table that points at your source files but does not copy the pixels - and it may or may not work in your groundwater flow model. But it has a number of options for deciding which pixels appear on top in areas of overlap - e.g. you can dynamically reorder the rasters by any available attribute (date, resolution, accuracy, etc.) and that may be of interest if you want to run your model with different rasters as "first priority". Or if you want to blend overlapping pixels etc.
You did not mention NoData regions, but I'm wondering if that is a related issue you'd need to manage...? At version 10.3, ArcGIS added a function called "Elevation Void Fill" that provides an option to dynamically fill NoData areas if that is an interest.
If your model cannot take a MD as input, I'd suggest you manage the various rasters in an MD and then once you have the overlaps properly addressed you can output a raster at any desired resolution & projection.
If you could describe your data & requirements a bit further, and let us know your version of ArcGIS, we may be able to advise with more specifics.
Cody B