Is there a way to add padding to the automated crop and straighten photos?

You example and your process description do not belong to together.

You first image look like you used a flat bed  scanner with a gray background to scan a print at 300 DPI print resolution. images 69348

You Auto process removed gray background straightened the Image a trimmed the Transparency image 69348auto

Your third image is  the auto image with a resized canvas  to make the image the desired 10" x 8" 300 Print size. 69348propper

The canvas Color can be any you want.

The was no cropping done there would be no borders added if the scan print was  10" x 8" paper  size can camg ams net bi be a perfect 10" by 8" in this case the canvas was sized up 101.46% of the scan sizeled the 1.5%. 

Action can not use logic to deal with image size.  Actions are recorded Photoshop steps the step are record on a single size document and the steps are record for that size image.  If all you scans are not of 10" x 8"  prints.  You will either need to use Photoshop scripting to deal with Image size, or record an action for each scan print size and batch process one print size size scan at a time. 

It is leaving the white border - you mean you want the extra black background in the images?? There is no way to do this with the automated crop and straighten. You could create an action to enlarge the canvas after the fact but you can't do what you are looking for in your propper image except by hand that I'm aware of.