Skip the Crop tool and use the Rectangular Marquee. In the top toolbar set Style to “Fixed Size,” input your dimensions (1000×378, in your case) and click in the new image. It’ll create a selection to that exact size. Now just drag that selection to the part of your image you want to keep, select Image>Crop, and you’ve got your new image in the exact same size.
If you have a bunch to do, you could also set up a Batch Action with a Stop set up after the selection is made so you can position the selection where you want it before letting the Action continue with cropping and saving.