Exporting to a set resolution does not export it to a set resolution

Open in Photoshop, fix the sizing, and export from there. This can be automated in Photoshop.

Precise cropping is difficult in Lightroom Classic because of the way it crops by aspect ratio only. If you need to export with absolute precision, you might try the AnyCrop plug-in (paid, but 30 days free trial):

https://johnrellis.com/lightroom/anycrop.htm

Another option is to use ON1 Resize. Or the AI Resize in ON1 Photo RAW MAX 2024, etc.

Are you cropping to 1408 x 792 before exporting? This can be done in a virtual copy.

Remember, in the Export Screen, when in Image Size, you select to fit Width & Height, LrC will create an image that fits within that Width & height, within that box. Either the Width or the Height will match the number you select, the other dimension may or maynot, it might be smaller. Depends upon width/Height ratio of image. LrC is not going to stretch the image to fit exactly in that box.

See if cropping before exporting helps.

This is because Export can unfortunately only achieve a "zoom to fit (within rectangle)" outcome rather than a "zoom to fill (entire rectangle)" outcome. 

Alternative 1 is to export to JPG from the Print module instead, which does offer a zoom to fill option. This is however no good for preserving individualised file naming, keywords etc into the output.

I would suggest alternative 2: add Postprocessing steps using a utility such as ImageMagick directly (controlled by commandline options) or else in the form of a LrC plugin (Mogrify) to trim off any surplus pixels present. So calling that in would be specified in your export settings, and made easily repeatable for the future by saving those settings into a named export preset. 

One more thought first: you are quite certain the identical aspect ratio of crop was consistently in place?

You can only export to exact pixel dimensions if your image has the exact same aspect ratio, because exporting will only resize, not crop. So in other words: let's say that the original image is 2000 x 3000 pixels. If you tell Lightroom to export a 200 x 310 pixels image, then you will find that this won't be possible. Lightroom can only export a 200 x 300 pixels image, or a 207 x 310 pixels image with these export settings (no idea which one it will choose). In Lightroom this might be quite difficult to achieve, because the crop tool does not show the crop in pixels. In Photoshop you can achieve this a lot easier by exporting a very slightly larger image (that you can do from Lightroom), and then use the Canvas Size option in Photoshop to cut this down to the exact pixel dimensions you need.