I want to go back to your original concept of cropping by matting. Why not just do the traditional approach...
1) Crop the image to the proportions you want, leaving a very small margin for mat overlap.
2) Resize to suit & print.
3) Use a mat and frame to suit the print.
You are sort of trying to approach it backwards. If you intend a crop, it should go to the print that way.
OK, on the cropping issue you are correct and it sounds so easy, but here is my thinking, and man is it a pain in the ass.
I use the Noritsu 3.xx printer, and it prints at 320 ppi. If I set my resolution to max of 8 mp at a 3:2 aspect ratio, I can resize perfectly for the Noritsu 3.xx printer in Photoshop for its 12 x 18 print size without losing anything in the picture. However, if I want a 12" tall photo that isn't as wide as the 3:2 aspect ratio, I set the camera to standard 8mps size and 12" tall comes out to 16" wide. However, the Noritsu doesn't print at 12x16. The next step down is 11x14. The problem with 11x14, which I hate, is that it gives unequal matting space in the 16x20 standard frame size, unless you have the matting cut to an unequal size, like 9x13 (so you lose more off the height than the width in order to get equal space all the way around in a 16x20 frame). You can't do much else because at a 13" hole, you only have 0.5 inch to play with for the width. For some reason, I hate that aspect ratio. On the other hand, a 12x16 print can be perfectly matted to have equal space all around in a 16x20 frame (hole size would be 10x14 or 11x15 which gives 3" or 2.5" all around, and 3" I think looks better). This is a more pleasing rectangle, in my opinion, than what you can get with 11x14 sizes.
So, in order to get a 12x16 print, I need to print on 12x18 paper. Can you see my analysis here? Perhaps I am over thinking the situation, but I really put my head to work and tried to figure it all out before buying matting and frames, etc. What I ended up with is 16x20 frames with matting that has a hole size of 10x14 and 18x24 frames with matting that has a hole size of 10x16. This gives a nice 3" and 4" all around for the 16x20 and 18x24 frames, respectively.
So, I can crop the images and print them at either size I guess, as long as the crop is not too far off the aspect ratio I am using, or I would need a different mat size or I would lose more of the image in either width or height.
My conclusion is that I'd rather compose the image as close to perfect as I can and avoid much croppping in the future. However, to answer your question, since I have 1" all around on either size image, I can move the image to the left or right, top or bottom as much as 1 7/8.
I was trying to keep the matting standard for cost reasons. I got the matting in white core acid free from Redimat.com for about 2.50 average each. Plus, I have to think about frame sizes too and space around them from the picture. Unless I wanted to use a nonstandard frame size, cutting matting with different hole sizes for each picture while maintianing the same space all around, or bottom weighting it even, would be a nightmare. So I just figured I'd use 16x20 and 18x24 frames, and then the matting I described above, printing both on 12x18 paper. I was trying to (1) keep price down and (2) standardize frames and matting.