I like the gear train idea. I like it so much that I have tried it in the past. My findings were that the backlash is almost impossible to mitigate and the friction gets pretty unreasonable.
I am a coach for a high school robotics team and we have learned that if you can do something with string instead of gears that is preferable.
Here you can see one of our robots. You can see that both motors sit on the base plate and we run string up to the elbow to drive it. I would suggest something similar for you. Have a small drive pulley and a large elbow pulley that is then connected to your noncircular DLCJ. I am drawing ovals for now but it will probably need to be something else entirely.
You are not limited to 360 degrees. The drive pulley can have the string wrapped around it multiple times. You can also fix the string to both pulleys so you are using just string tensions to drive your arm and don't have to rely on friction.
I am a coach for a high school robotics team and we have learned that if you can do something with string instead of gears that is preferable.

Here you can see one of our robots. You can see that both motors sit on the base plate and we run string up to the elbow to drive it. I would suggest something similar for you. Have a small drive pulley and a large elbow pulley that is then connected to your noncircular DLCJ. I am drawing ovals for now but it will probably need to be something else entirely.

You are not limited to 360 degrees. The drive pulley can have the string wrapped around it multiple times. You can also fix the string to both pulleys so you are using just string tensions to drive your arm and don't have to rely on friction.