That will insert a new caption, yes. But then I have two captions showing, one reading "Fig. X.X" and one reading "Figure X.X blah blah". I want the image to keep the caption reading "Figure" but have the reference in the text read the caption "Fig.". Any ideas on how to do that?

From my understanding, you can only change formatting.
Once you set up the caption as "Figure X.X", then if you recall it in the document (using cross references) you cannot edit the content (Figure X.X), just the formatting (as detailed here).

You can do this easily. Click where you want to insert the reference and type "Fig. " and then insert the cross-reference by inserting the paragraph number only. As add figures you can update the figure numbers using F9, while the label remains "Fig."

I also want to change Figure to Fig. throughout my long (already written) document and I'm somewhat stunned that this is not easy to do. As someone mentioned, formatting the labels can be done globally but not so with editing the labels? So, do I have this right: My 'best' option is to remove the label "Figure" from each reference so that the fields contain just the numbers and then I have to go back and manually type in "Fig." everywhere!? After 14 versions of Word, this is what I'm left with?

If you want to use Fig. and Figure, then you'd better make one fixed - e.g. the field being "Figure X", while for the others, the field would be "X" only, with "Fig." typed manually.

Word runs on a computer, it can't read your mind and guess when you want to use Fig. or Figure. Give him a rule, and it'll follow it 'til death, but don't ask it to guess your thoughts.