Hi there and
to the forums!
Are your double factor cocks ino (i.e two copies of the ino gene) or double factor crested? Are the red eyes crested single, double or crestbred? Are they actually Ino or do they just have red eyes (i.e are fallow)?
Crested and hagoromo budgies apparently are in possession of a very strange gene, which, although autosomal dominant, only acts dominant in certain cases. If you have a double factor, it will be visual, but if you have a single factor, although it still has the dominant gene, it only will show the gene 15-20% of the time. So you could have a bird that visually looks normal but actually is SF.
Apparently, the best way to breed for one with best possibility is to take a known DF (either from two visual parents, or with very noticeable feather) and breed it with a SF hagoromo, or a normal, both of which should be the result of hagoromo parents and both which are indistinguishable from one another as the gene appears to be lacking entirely if the SF does not express the visual trait, much like the normal offspring of a SF and SF, which could be a normal.
Basically any chick from a visual pair who doesn't show a visual trait could have one gene, making them SF, or zero, making them genetically as well as visually normal, but unless you knew the exact genetics of the parents it would be almost impossible to tell.
Although you could breed two hagoromo budgies together, by breeding it with a visual normal it cleans up the genetics a bit so it's not as cluttered, similar to the reason you don't breed two inos together.
However, both parings will yield crested budgies, DF x DF and DF x SF. With a visual male and a normal female, all the chicks will be either single factor or not have the gene at all. Technically, if the father is DF, all chicks will be SF by default, but unless you know the father's lineage that's impossible to tell.
Because the gene only shows up sometimes even though it is dominant, you could get all SF chicks and none of them would ever show the trait. The only way to know if a chick is SF or normal when they don't show the trait is to breed them in the future with a normal and observe if they pass on the gene.
You should never breed two Inos (visual ino) together because it brings a high risk of health problems such as poor vision and other harmful genetic defects. Because Ino is a sex-linked gene, you'll need to breed a cock that is either split for Ino or is visual Ino with a non-Ino female, which will get you some female chicks that are Ino. The end pairing you need to get Ino hagoromo budgies is a visual or split Ino cock that is a known carrier of a hagoromo gene (either DF or SF) with a normal female which is SF for hagoromo. Despite the chance being slim, there is a chance you'd get a hagoromo female that is also Ino.
Hopefully that answers your question.
Meanwhile, be sure to familiarize yourself with the forums by reading through all the links provided above by FaeryBee! It's important to stay up to date on the very best of budgie care practices to ensure your little ones get the best care possible. If you have any questions after reading though everything, please be sure to ask as we'd love to help!
Hope to see you around the forums, we'd love to meet some of your budgies when you have a chance!