The change of stamping on body tag from "Body by Fleetwood" to "Body by Fisher" occurred in 1965 despite the carryover body style.
Here are the body tags from a 1964 and 1965 Series 75.
(https://bringatrailer.com/wp-content/uploads/2020/10/1964_cadillac_fleetwood_75_limousine_1607051120218fc5c82C8B2B4E-73CC-4DCA-B3A5-5B07A65F7ECA.jpeg?w=620&resize=620%2C413)
(https://bringatrailer.com/wp-content/uploads/2023/09/1965_cadillac_series-seventy-five-factory-limousine_id-tag-44238.jpg?w=620&resize=620%2C413)
I have parted 40 1964 Cadillacs, including a couple of 64-6723's like in the first body tag and a 64-6733 (formal limo). I have saved the body tags off most of them and did a spot check of a lot of them and it appears that all built before the 1st week of Oct, 1963 (as noted by 10A in the original posters top body tag), had the inscription "Body by Fleetwood" at the bottom, but by the time you get to the 2nd week of Oct, 1963 (10B) it had switched to Fisher and continued to note as body by Fisher for the remainder of 1964 model year, regardless of body style, including the 75 series.
I have parted 20 1963's and went back and spot checked a half dozen of those targeting different points in the production run and they all stated body by Fisher at bottom of body tag. So it seems they started out indicated Fleetwood on early 1964's then switched back to Fisher by 2nd week Oct 1963. This is of course a best guess on a sample, albeit a reasonable qty of samples.
Thanks Jason for that information- narrowing the change within the time frame of one week is about as good as it gets.
The lingering question is when the same change occurred for the Sixty Special. Would you happen to have any insight on that?