My active area is smaller than yours by about 20mm each way, and I use my arm!

How large is your monitor? A smaller monitor gives you less space to work with. Mine is 24" and I feel like that helps. This might be out of your control - then unfortunately you will end up only able to use your wrist for most strokes.

It seems impossible right now, but you CAN ghost on a non-display tablet. You need to follow the motion of your cursor using your eyes while you make the movements, using all the same fundamentals that Uncomfortable outlines (heh) in his markmaking lessons. Confidence and precision. A bigger screen also helps with this.

Allow yourself to fall on your face and keep sticking to drawing with the arm. Practice practice practice.

If your machine and can handle it and monitor can display it: Don't draw small. Your arm is allowed to start and end outside of the active area. You can do a big swipe over it. These movements will eventually feel natural!

I still rely heavily on the wrist. The same way you need the wrist to draw small detail on paper, you need the wrist for small details on screen. It's around 30/70 arm:wrist ratio.