if the Rose he met was angry and very unhappy, or if she was of the opinion that the proper Doctor didn't really love her, he might be so horrified as to attempt to change the timeline.

Precisely.

He adores her, he’d do anything (including changing time) for her.

Besides, he might be able to save Donna, too, depending on how he goes about it.

That, my friend, is a Very Good Point (and one I’d completely missed somehow).