I think that the bottom line is this:

If you have an AA reservation that codeshares with JL, then the seat assignments must be made by AA.

I had an exceptionally helpful JL agent in my experience mentioned above, and she explained to me that the JL system just did not permit her to make the seat assignments on AA reservations. Instead of sending me back to AA, however, she made the call into AA for me and secured the seats.

A JL agent may tell you one of these three (3):

(a) To call AA and get the seats assigned there;
(b) To wait until the online check-in, 24 hours prior to departure; or that
(c) S/he will call AA on your behalf to secure seats

I was lucky to get the (c).