The problem is that the owner does not know what their turkeys are. The colors that are showing from the pictures that you posted are not possible results from what she told you.The owner of the turkeys told me that. She said the toms have same father different mothers and the hen is entirely unrelated. She says the toms are blue slate/royal palm and the hen is blue slate/red bourbon. I do agree that the hen looks more like royal palm than any of them!
This one appears to be a Rusty Self Blue (BB DD Rr).
Each of its parents had to have at least one dominant slate (D) gene. And one of its parents had to have a recessive red (r) gene. Royal Palms do not have either of those genes. One of the parents was probably a Blue Slate (BB Dd) and the other parent was probably a Rusty Blue (BB Dd Rr).
The top tom in this pic is a Red Bronze, probably (bb Rr) but there are other possibilities such as (bb1 Ccg Nn Rr).
I see no evidence of it having any Blue Slate in its parentage. It could have Royal Palm in its heritage but also needs to have inherited at least one recessive red (r) gene to make it into a Red Bronze.
The hen at the bottom looks like a possible Golden Narragansett (bb1 Ccg n- Rr) but could be a Narragansett Semi-Color Semi-Gray (bb1 Ccg n-). Either way, it does not have Blue Slate in its parentage and definitely has Royal Palm it its parentage.
When you cross a Royal Palm tom with a Blue Slate hen, you don't get a Blue Slate/Royal Palm cross. You can get Barred Black Semi-Color Semi-Gray and Tri-Color Mottled Slate toms and Barred Black Semi-Color Semi-Gray Narragansett and Barred Semi-Color Semi-Gray Dilute Lilac hens.
If the cross is a Blue Slate tom and a Royal Palm hen, you can get Barred Black Semi-Color Semi-Grays and Tri-color Mottled Slates.