Here's a patch that ads Resample Method to the Fit Image. It works with Fit Image 1.0.0.21, which is shipped with Photoshop since CS5 at least.
It shows only available modes and defaults to: "Automatic (CC)", "Bicubic Automatic (CS6)", "Bicubic (<=CS5)".
The patch and description are on my blog: http://sepczuk.com/techblog/2013/07/fit-image-extended/