Cannot make a crop preset actually crop to the same image size for multiple images

I know this should be simple, but I've struggled with trying to get the crop preset to actually do what I'd like.  I have tried reading many of the discussions about cropping multiple images, but have not found the answer yet.

I have hundreds of photos of a solar eclipse that I want to crop to the same size.  The center point is not the same in each image (do not have a tracking sytem), so I need to slightly move the crop area for each image.  I have tried to save a crop preset for the first image (multiple variations), but when I apply it to the next image, it always wants to crop a larger portion of the image.

I'm not trying to batch this, as I need to move the crop area for each image.  I have tried in the past to load the images as layers but exporting the layers as files changes the time stamp of the image to that of the first image.  I want to preserve the actual time stamp.

Any help appreciated!