In my experiance, modelers often have no idea what coordinate system their models use.
I have had to create points from their raster cells (in an 'unknown' coordinate system)
preserving not only the lat and long data the cells provide, but also the x and y position of the cell in the original raster.
Withe the lat and long positions, I can plot the points in geographic space
(and project it to projected space) and use it as I wish. I assume that this is what you do, too.
But, because I have also preserved the original x and y locations
(lower left = 1,1 and upper right = max x, max y)
I can go back in the other direction (known projected or geographic space to model space)
by using an insert cursor to build new points (with the new attributes I have added)
using the original x and y locations.
This gets the points back in the proper places in unknown space to make an orthogonal raster from them.
It is a bit roundabout, but if one don't know the model coordinate space
or if the model coordinate space is one not supported in Arc,
it works.