Yes, the 1.5A controller would be quite well suited to the 1.7A motors. Unlike regular motor control where the controller must have a much higher current than the motor, the stepper controller is the "policeman" who controls the current. So it will be able to drive those motors quite well, but not to their absolute maximum.
Yes, your torque calculations seem correct although I have not put the numbers into my spreadsheet to check. You do need to allow a lot more than 1/3 for friction losses. With the belts and gears shown in your pictures, the losses will be higher.
Also remember that the stepper manufacturers always quote the holding torque, not the moving torque. It can hold 4kgcm if someone leans on the camera but it can't accelerate the camera upwards if that is the static torque. I would allow at least 50%, particularly since you aren't driving the full 1.7A through the motor.