Do you have a microcontroller in the system already / anyway? Almost all microcontrollers can easily provide a current-limited control for a brushed DC motor with a few dozen lines of code (utilizing PWM / analog comparator / ADC peripherals), and this is usually a better way than to add an extra "motor controller" IC, some of which are completely unusable, some difficult to control, and - finally - some probably fine but not much easier.
For such low-voltage, low-current design you would just create H bridge out of two N and two P-channel MOSFETs, gates can be driven directly off the microcontroller. For current sensing, a separate shunt resistor + sense amplifier IC on both ground legs is probably easiest. When changing direction, you can at the same time change which of the current sense signals is routed to analog comparator peripheral. Then configure the analog comparator output to terminate PWM cycle, possible in many microcontrollers (e.g. the whole STM32 series including the lowest cost items), or if unavailable, let it generate interrupt and limit current in software.