I don't think that Photoshop has a way to fit the image to the frame the way you'd like. You can submit a feature request to Adobe.
In the meantime, would it work for you to create an Action that converts all of your images to the height and width of the frame -- then, after all the images are resized and stored in a folder, place them into the frame?
Image > Image Size command can disproportionally resize an image.
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