How did you link the cover art files? If you just link an image file manually you can keep the original name and location.
As you said, video cover art should have the folder options (specific folder / next to file) separately from the audio cover art options. Because video files don't have an established tagging standard the used filename should be just the video's actual filename with a different file extension (jpg, png, etc). In case of name conflicts MC should use the standard MC style and add (1), (2), (3) etc.
Personally, I have only a few video cover art files. I've had no problems with naming the files manually. For example, ripping and compressing a DVD can take hours, so it really doesn't matter to me if downloading or scanning a cover art file and manually naming it takes a couple of minutes. Adding a video movie to my library is never a simple background task like ripping audio CDs.