I gather that what Michael is trying to attempt is to crop images to end up with any size (in whatever units he works in) at the 'native' resolution. He doesn't care if the end image is 6 units by 9 or 6 by 4 or whatever as long as the pixel resolution does not change.
Here is what happens in the real world:
I open an uncropped image from ACR (from Canon 5D2, 16 bit). The Pixel Dimensions (file size) is 120.3 mb, (5616 by 3744 pixels -- that is what the camera sensor produces)
The document size becomes 112.32 by 74.88 picas at 300 pixels per inch.
That also happens to be a 2 by 3 size ratio.
Since I will be printing on 13 by 19 inches paper and want to start with non-fractional units, I change to document size to 108 by 72 picas in the Image Size panel, having deselected the Resample Image check box I end up with the same pixel dimensions but now the resolution is 312 pixels per inch.
In Preferences (Cmd-K on a Mac) I make sure that my units are in picas (you can choose whatever unit flavour you prefer).
Now let's use the crop tool.
First I simply go for the crop tool leaving all the boxes (width, height and resolution blank). I crop an area measuring 90 picas by 60 picas (2 by 3 ratio) -- use the Info panel to see the measurements. That makes for an image with the following dimensions: 83.6 mb, 4680 by 3120 pixels; 90 by 60 picas document size and 312 pixels per inch resolution. There has been no resampling, I simply used a pair of scissors to cut out a smaller image from the larger one. If I crop a smaller area, say 36 picas by 24 picas I will simply have a smaller 13.4 mb, 1873 by 1249 pixels; 36 by 24 pica document at 312 pixels
I enter 90 picas and 60 picas in the width and height boxes but leave the resolution blank.
I use the crop tool and drag an area to be cropped. The tool's marquee is proportional to the 90 by 60 size. I adjust the box size and location to my liking and Enter.
This, in this particular case, gives me an image of 55.4 mb, 3812 by 2541 pixels; and a document size of 90 by 60 picas and a resolution of 254.133 pixels per inch. There has been no resampling. A different crop will produce the same document size but with different pixel dimension and resolution.
This time I enter 90, 60 and a 312 ppi resolution.
Crop, it does not matter what the actual cropped area is the following sizes will be always the same -- whether your crop area is tiny or larger -- the sizes will always be:
83.6 mb, 4680 by 3120 pixels; 90 by 60 picas and 312 pixels per inch. In this case you are enlarging the cropped area to the 90 by 60 picas size.
The crop tool will always use the units that you set in you preferences. You cannot change the units, say inches instead of picas in the boxes. The width and height boxes must be in units -- pixels, inches, cm, picas... you cannot have a number and no units.
So, you cannot set a crop ratio parameter in PS. You can only crop using sizes you set yourself; you have to figure out if the crop area fits you desired ratio by doing a manual calculation.
The easiest way to crop using a set ratio is to do it in Camera Raw, I don't know if Lightroom or Aperture have similar tools.
I hope that this helps and does nor muddify!