Another idea for preventing tangles is interlocking the mane gear with the power switch.  

Testing of the 1st joystick revealed the motor is too hot at the required current.  That might be all for the brushed motors.  Testing of the joystick could be done with manual means.  There are but 2 L6234's left in the apartment.  

Tape decks used a clutch to provide constant tension to the takeup reel without stalling a motor.  

The clutch was 2 plastic disks pressed together by a spring.  The disks were lined with felt.  This provided very little torque.  Brushless gimbal motors should be able to replace this.

The right angle required in the joystick creates a lot of friction & fraying of the string, which causes it to jam.  The resistance increases as the spool diameter shrinks.  It needs a pulley.  If it's going to use a pot, the pot needs to have no friction.  There's a big deadband where the string isn't pulling sideways enough to move the joystick.  

Another idea is having the complete motor spool assembly on the end of a pivot, electronicals & all.  That eliminates the right angle, creates a lot more leverage against the deadband.  It folds 90 deg for storage.  It requires a large pivot.  The feed hole could point diagonally.