There are many companies who do do dedicated chips for stepper drivers. The A4988 has a step+dir digital interface. If that's what you want, then you could for example use the Texas Instruments' DRV8825
I was myself looking at different ways of interfacing stepper motors (not just step+dir), and made a comparison table of stepper motor drivers.
That driver will work fine, provided you use a proper power supply.
The allegro stepper-drivers are current-limited chopper stepper drivers. As such, you only have to ensure the power-supply voltage for the driver is > then the rated voltage on the stepper, and you have set the current limit properly.
Basically, chopper-stepper-drivers actually modulate ("chop") the drive voltage to the stepper in real-time to maintain a fixed coil current.
The ratings for your motor are steady state. Basically, it says that if you apply 2.55V DC, 1.7A of current will flow though the motor coil.
However, the Allegro drivers don't apply DC, they apply a duty-cycle modulated square wave, which limits the overall power delivered to the motor.
Functionally, the driver will vary the applied voltage to the stepper to maintain a fixed current (it's not quite that simple, motor inductance is involved, but it's a reasonable simplification). As such, as long as you're not applying more then 1.7A of current to the motor, it will work fine.
Basically, the simple version is the motor ratings are basically constrained by the thermal behaviour of the motor. If you apply too much power, it'll get hot enough to damage the motor.
With the A4988 driver board you link, you can vary the motor current by adjusting the tiny pot, which allows you to adjust the motor power to whatever you'd like.
If you run the driver off input DC within it's operating range, you will be fine.
Best Answer
I'm not sure what you mean by 'the limit setting potentiometer', but (assuming that you mean the current sense resistors \$R_{S1}\$ and \$R_{S2}\$ (which would be an interesting design, those should be matched low-impedance resistors) I read on page 9, in the section Internal PWM Current Control:
Do you have access to the REF pin (pin 17)? If so, adjusting this with a DAC will produce the same effect as varying the sense resistors.
If not, the Enable input is probably a better choice than cutting the power or using the sleep or shut-down pins, those would incur a 1 ms delay (per the description on p. 10).