I'm not sure I understand what you're trying to do. Many of settings for a title don't apply in any way to an image, like font, line spacing, size, etc, so the normal way of using Copy/Paste Keyframe Attributes isn't available.

If it is just to reuse the text box, or title again and again with the same settings, why don't you make it a custom title? That preserves the settings and can be used again and again? And the text can be changed.

if you need to reuse that text as created, why not put this text in front of a green color board and make a snapshot. The shot can be used again and again, even in front of a clip, by removing the green?

Sorry, to clarify I'd like all the same non-text keyframe settings without recreating them. Scale, position, opacity, etc. Essentially I want the exact intro video I already have but with my actual logo instead of my company name in text.

Perhaps I can't do what I want. It looks like motion is only available for titles, not images.

It would really help if you could show us the current intro video because I'm still unclear on a lot of things.

It sounds like you could simply change the text in the existing title, but I don't know what kind of motion you're referring to. Is it simply changing the position with keyframes?