How can I include value of Sharepoint's Modified or Modified By column in a Word document?

Question

I know how to do this with SP's Version field (by enabling labels in the Information management policy settings for documents in my SP library), but I don't know if any other out-of-the-box SP fields can also be used as a label.
I specifically want to use the SP Modfied and Modified By columns, but when I try to input {Modified} or {Editor} or {Last_x0020_Modified} or {MyEditor} or {ModifedBy} into the label format field in the Information management policy settings, I get the error
(this error is what is shown when I tried {Modified}):
There were errors on the page: The label reference, Modified, can not be used in a label.
The only field that seems to work as a label is {Version}.

Answer 1

Whoops! This is partially my answer, at least for the SaveDate. But I'm having a problem with the
LastSavedBy field.
What I'm trying to do is have both of these in the header of my documents in my SharePoint library. So I've made a Word template for the library that uses your solution in the header. When I first open a new document, the
SaveDate looks like 0/0/0000, which is right because that's the format I chose and I haven't actually saved the document yet.
The LastSavedBy is blank, so I figured that was correct, again because I haven't saved the document yet.
After I save the document, check it in and then open it again, the correct
SaveDate appears.
I figured the same thing would work with the LastSavedBy field. But it doesn't. When I reveal the field codes, it is correct: { LASTSAVEDBY  \* MERGEFORMAT }. I know that's correct, because if I manually delete that field but then add
it in again, it THEN appears to work consistently.
If I use the Author field in Word instead of the LastSavedBy
field, it works perfectly. But I assume the Author field is SharePoint's
Created By column, and I don't want that. I want the Modified By column. But I can't get that to work in the template the library uses. So It's useless to me, unless I train all my users to manually insert that Quick Part for
every new document they create in the library.
I'm figuring the problem above has something to do with a new document initially not being saved or checked in, but I don't know if anything can be done to correct this.