I helped a guy fix some knobs for a radio that were made of similar construction and I am going out on a limb here but I think how they are made is by first turning the knob then the intricate center portion is made of repwood which is basicaly wood dust and a binder, likely hoof glue. Fada was good at using repwood and the parts really do look like wood, it is hard to detect that they aren’t wood but rather, "repwood". Carving a pattern like that would be extremely labor intensive and they were good at using repwood to simulate that intricate carving. They likely had a wood carver spend hours to make the original , then all the others were molded from that pattern.
the guy I helped, provided me with one good knob which was a sample. From that I ground a steel blade with the same outer contour. I turned several knobs to work with (on a metal lathe) once I had my specially shaped knife made. the center is recessed to accept the repwood piece. i drilled the recessed area out with a forestner bit.
I then gave him the knobs back. He made a push mold, it worked out well but it was a lot of work.
So for example take the good one, lubricate the sample so it doesn’t stick and ( to make a push mold) push it into your mold making material, which could be plasticene or perhaps that wood putty the kind that you kneed together and it hardens. You could use epoxy, or there is that fake wood stuff that they sell in Rona which is like two film cans A and B stuck together and you mix the stuff, (PC woody it’s called). there are many other types of material that you can use to make molds.
A medium that might work well to replicate the center repwood portion is "Femo" , which I found in an appropriate dark brown color at michaels ( the art supply store) I think there is a competing brand called "Premo". both are a plasticene like material that you can shape and then you harden it by cooking it in the oven at a low temperature. There are specific mold making materials on the market if you look for them, but they get a bit expensive for one off jobs. Latex rubber might work for a mold. You need to be careful that whatever you use doesn’t get all stuck into your sample knob. even silicone rubber may work as a mold making material but it takes a long time to harden if it is a large blob.
You can paint on silicone or latex rubber for an outer skin then drop that into "plaster of Paris" Using this idea you can create a mold that is mosly plaster of Paris but the actual part that takes the form is something softer like latex rubber. You can look at the materials used by dentists and dental labs if you have a friendly dentist, dental technician, or dental mechanic that you know, such as the pink stuff they put in the little tray, and push into your mouth.
there is a lot to mold making. sometimes a softer rubber is needed to take the details of the mold and for it to be possible to separate the sample from the mold and to get the finished piece out. sometimes it is necessary to pour the mold in more than one layer to get the piece out. with the materials above and a bit of thinking and experimenting there is a lot that can be done.
It is also possible to make a mold of the good knob and make a new one from epoxy, colored dark brown. if the mold is good enough it can pick up the wood grain and look very realistic especially if some paint is rubbed into the grain to give it that tonal variation.
Whatever materials and process you decide upon the task is to replicate the little repwood buttons using the original good one as a pattern, once that is done you glue it into the recessed area of the knob. I think what has happened is that this knob was probably banged against something and the repwood portion has fallen out.
Some material is lost on the outer knobs but you might build that material back with wood putty. The epoxy type might work well for this , such as the two part wood putty that you kneed, it becomes plasticine like and then it sets up. that stuff is more durable than just regular wood putty.
You might make a mold of the good knob , add a bit of material to fill the voids on the damaged knob, and then place that into into the mold made from the good knob, to force the putty into only the areas where material is missing. Otherwise you could just fill the voids and carefully sand the contour.
by the way. this is off topic, but It is possible to repair small broken gears with a few broken teeth by making a mold of most of the good teeth then turning the gear and placing it back into the mold along with a glue or epoxy or JB weld or something. this way it is possible to replace only the missing teeth by using a mold as a form to make more teeth. you could use the same idea to replace the bad portions of your damaged knobs.
If you are using wood putty you can tint it to get the right color by adding a colorant. I often use the powdered pigments available at Mohawk finishing supplies. I add this to my wood putty to get it the same color as the wood. Most wood repairs that are obvious are because the color of the putty doesn’t match. you need to think ahead and experiment because putty won’t accept the finish and any stain etc in the same way as the surrounding real wood does. you can also use wood touch up pens just before laquering to hide sins in wood filler mismatch. I often mix more than one color of filler and blend them together to simulate grain. wood is never the same tone all the way through and if the filler is monotone it will show. wood also usually has some knots and imperfections so by blending different colors of putty, you can make really invisible repairs quite easily, if you get the colors exactly right. I’ve been pretty successful at doing this by surrounding the damaged area with masking tape , then applying filler, after I get the filler on I smooth it level with the masking tape and pull the tape off. this leaves the filler a few thou higher than the surrounding area to facilitate sanding. the smaller the area covered by the putty repair, the less it will show, so surrounding the problem with masking tape limits the size of the repair. You don’t want it larger than it needs to be.
All in all it was quite a task to come up with a repair and I see this and think it is quite a similar task. Other knobs might be the answer. If you are really set on having the knobs original you might take some ideas from above.