I did some further digging about the European cuckoos. There is debate and confusion there as well. This was from a forum where most of the guys are there are from UK, Mainland Europe and Australia.
There are 3 versions of cuckoo in the UK. Dark, Silver and Golden. As far as I can tell, the Golden and Silver are Barred BCM and Birchen, although it is also argued that the Golden is supposed to be Crele, but that very few Golden Salmon (wildtype) birds exist, and almost none have good type, so creating true Goldens is next to impossible.
At least I found a description from UK standards:
Golden Cuckoo female
Hackle medium bluish-grey with golden and black bands. Breast dark bluish grey with black bands, pale golden shading on upper parts. Remainder dark bluish-grey with black bands.
Silver Cuckoo female
Mainly white in neck and showing white on upper part of breast. Remainder banded throughout. Lighter ground colour than the Dark Cuckoo.
Golden Cuckoo male
Male Plumage:
Hackles bluish-grey with golden and black bands, neck paler than the saddle.
Breast bluish-grey with black bands, pale golden shading on the upper part.
Thighs and fluff light bluish-grey with medium black banding.
Back Shoulders and Wing Bows bluish-grey with rich bright golden and black bands.
Wing Bars bluish-grey with black bands, golden fringe permissable.
Wing Primaries dark blue-grey lightly banded.
Secondaries dark blue-grey lightly banded with slight golden fringe.
Tail dark blue-grey banded with black.
Coverts blue-grey banded with black.
These descriptions, if we are going by British Standards DO describe birds with birchen ER. The Dark Cuckoo is the one that doesn't have a lighter hackle, and that should be EE based like Barred Rocks. But I don't know if the U.S. cuckoo should be based on the silver or the dark British Cuckoos, the french sources don't give any useful information to determine genetics, and are rather disappointing.