Liandralithe, I'm not sure if someone has messaged you already to tell you this, or if you already knew this and I just misunderstood you, but the Breeding Offers already has a feature that can be used in this way with beasts that have been researched.
Next to the Search:, found above the first pet listed and to the right, you see a [+] like in the Pet Auctions. If you click this it opens up the Search Menu where you can search for a maximum of 2 genes in the genetics section of it, and 2 is all you need to search by color/pattern.
To do this, first select the species you're looking for, since that will limit the gene search to only the genes available for that species instead of cluttering the menu with all of the possible genes in the game, and then search the genes you need for your preferred stud; in the case of a White Gyrfalcon Roc you would want to choose White as the Skin Color for Gene 1 or 2, and select Bird of Prey in Skin Pattern for the other. Then what you want to do is select "All checked" to ensure the studs that come up will have both of the genes you are searching for. There is currerently no Homozygous Gene option to show only beasts who has this gene as both thier recessive and dominant, but if you select Only Dominant it will bring up only the beasts that show those traits for their skin.
Now, when you select a female to breed straight from your stables you then have 2 of these Search Menus. 1 is above your males and searches only through them, while the other is above the males listed in the Breedings Offers and searches only through those ones.
I hope I explained myself clearly enough and was of some help! I actually just posted a suggestion regarding the search menu. Or rather, 2 suggestions in 1 forum; 1 that will add the Search Menu to stables so you can search through your pets that way, and a second suggestion that involves refining the menu to include more options (such as a Homozygous Gene option).
