Yes ,
certainly, mechanical solution is necessary, a purely elctronic solution will be very difficult ton install and the parper will be broken.
See the old tape recorder, the tape goes on a spring loaded 3rd axis. This piece have 2 funcion: first it will compensate short time difference of you 2 axis speed and secon: the position of the axis is measured ( optical or mecanical solution ) and control the speed of the "slave" axis.
Stepper motor are a good solution beacause you can easyly control the output stage of the slave motor.
In my opinion, Allegro ICs are very good. For example the A3977 is excellent and can control bipolar motor in u-step way offering a smooth operation.