@MysteryChicken I have a few ideas you could use to test your theory- they aren’t necessary, but they may help you.
You believe the mother of Squeakers, a mille fleur d’uccle, carries the dominant mottling gene, correct? So, her offspring should theoretically show mottling, no matter what. To test whether she actually has a dominant mottling gene, you could breed her to a solid or almost completely solid rooster (who isn’t white) which you know has two gold genes. That would eliminate any possibly of silver in her offspring.
Also, to test whether the OEGB father carries a recessive mottling gene, you could cross him to a solid (black/blue/lavender/etc) mottled hen.