Dustin, you are bringing up a very good point (maybe a problem.) We have had some discussion about this picture sizing issue in at least one other topic: https://moodle.org/mod/forum/discuss.php?d=372723#p1502738.
I think that I know what you are going through. The logic for sizing these images is not quite clear. What I have found is that the displayed image changes based on the size of the browser window. I too could not get this image always showing properly. There might be a lacking feature that says something like "keep image fully shown" or "maintain aspect ratio," or something like that. Since the current moodle is "responsive" there is some logic to resigning based upon the user's screen size. But something is not quite right with the dashboard images.
In a quiz that contains an image, I use a "responsive" template for the image. This allows the image to always resize and show in full. But this doesn't happen for the dashboard's course images.
Well, in my case I live with what I get. It has not been worth my time pursuing. But I can understand you Marketing department (Marketing folks want to be in control. )
Maybe you have already found a workable solution. I am just sharing some of my own thoughts.