Most of those pen controllers or shields are o.o expanded or own generators. In this case, the resolution maxes out to be just shy of 8 bits.
There are better ways to do it. I can post the link later but I explored quite a few ways to drive multiple servos off of a timer on a pic or avr. The number of servos it can drive is determined by the length of off-duration a servo can tolerate, and number of gpio pins on a mcu.
here is the link: https://dannyelectronics.wordpress.com/2017/02/18/driving-multiple-servos-off-a-pic-timer2-ranged-extended/
it provides a few examples for its implementation on PIC and AVR. But the basic concept is the same.
No shield used and it runs in the background so it is full transparent to the user code.