After much searching, I found the answer to my question. There is a function called
cmap2gray
that was introduced in R2020b (and I was using R2020a so I didn't find it right away).
The map which is output when you use the colormap function on a grayscale image is an "RGB colormap" and can be converted to a "grayscale colormap" by running
newmap = cmap2gray(map)
The 3 columns of newmap are identical (which is what you would expect). Now, I can easily convert my grayscale image which is originally black to white, to black to green by zeroing out the R and B columns in the newmap variable.
I can then apply this corrected "grayscale colormap" to my grayscale image to get it to display in green.