I have not done it, but I have read about the genes involved.
The dilution gene is on the Z sex chromosome.
A goose has ZW, so a Pilgrim goose has one copy of the dilution gene, and she passes that only to her sons.
A gander has ZZ, so a Pilgrim gander has two copies of the dilution gene (which makes him look lighter), and he passes one copy of it to each gosling he sires (no matter what their gender.)
If a gander has a Pilgrim mother but a Toulouse father, he should have one copy of the dilution gene and one copy not, so he will be colored like a female Pilgrim (diluted, but not as much as a gander should be.)
If a goose has a Pilgrim mother and a Toulouse father, she gets her Z chromosome from her father (no dilution), so she should be colored like a Toulouse.
So goslings with Pilgrim mother and Toulouse father should be sex-linked: dark daughters, light sons. If you cross a son to his mother, you should be able to produce some proper Pilgrim-colored males, along with single-dilute males, Pilgrim-color females, and Toulouse-color females.
The white in Embden is caused by having dilution and spotting both on the Z chromosomes. So the Embden gander would sire white goslings of both genders.
If you want to eventually have more autosexing geese, I would work with the Pilgrim and the Toulouse, but not the Embden.