I suspect, based on the images, that you are going to want to do some sculpting, assuming that you want some of the small textural details as are present in the gray patches in the wings. Rhino could certainly be used for the underlying ring shape, and also perhaps for the basic feather shapes, as it does an excellent job modeling smooth, curvy shapes. And it is the best program I have ever used for drawing 2D curves and shapes, far better than Illustrator, in my opinion.
The approach I would probably personally use would be to create the base ring shape and stone in Rhino. I would also maybe create the basic overall shape of the feathers/wing in Rhino, but flat, and then convert these to a mesh using QuadRemesh in Rhino. You could create each feather by drawing 2D curves and then making a trimmed surface from these and then adding some thickness. You could then basically arrange them, layering them each at a slight angle relative to its neighbor. Once you have all the basic shapes, you could try to make a boolean union of them and then QuadRemesh, or use the new ShrinkWrap feature in Rhino 8 (should be released by the time your trial version expires). Or you could keep them separate and convert to meshes, to be combined later.
I would then take this mesh data into ZBrush or Blender as an OBJ and add details/texture, if you want that, and then place the wings and bend them into position in Blender. Blender is the best tool of these three for manipulating the mesh and bending it into position, in my opinion. ZBrush is rather hard to bend things nicely with. But if your mesh is very dense, you will need a fast computer to manipulate it in a smooth and fluid manner in Blender’s edit mode using the proportional edit mode. ZBrush can handle denser meshes on less powerful hardware for reasons I don’t fully understand.
It isn’t entirely clear what you want to happen three-dimensionally with the wings. A 3D modeling app (or even modeling clay or wax) can help you to explore that and solve problems that maybe aren’t apparent in 2D. I would guess that the casting houses might have been reluctant to work with these designs because they are 2D and it isn’t clear how the wings should lay around the stone and one another and what should happen on the backside. It seems like it could be challenging to make the design work with two wings only. If you solve these problems in 3D and present the design as a 3D file, it would much better communicate your intent, which would make things far easier for them. Otherwise, they would have to do most of the design work for you.
Sometimes, when in only two dimensions, you can imagine that something should work that actually turns out to be problematic in three dimensions, and once you try to make it in 3D, you immediately see the problems. That’s one of the beautiful and powerful things about CAD and other 3D apps. You literally learn to think with them about 3D problems and to solve them. Such tools aren’t only tools to realize ideas you already have, but also tools to think with and to solve problems with. Our mental visualization ability is only so good, and we can only keep track of so many things at once in our minds. It is similar to how working out math problems on paper helps you do much more complex things than you can do mentally. If you can make it work in 3D on the computer, it will make sense also in 3D in the physical world. But there are other problems still with actually realizing something, as it needs to have a shape that can be cast, depending on the casting method, unless you are going to 3D print everything.
It will take a little while to develop the skills to realize your ideas in 3D software. But don’t be deterred! While you are learning, I would seriously consider using a stiff clay or wax to further explore your ideas. I have enjoyed using Monster Clay in the past, the hard version.
If you have a late October deadline, I don’t know. Sufficiently learning all this software and 3D modeling principles and techniques in general in that amount of time if you have zero experience with 3D is unlikely. You might want to hire some help!
I hope this helps! 
