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.
You don't say it, but your problem may be that you're trying to start the stepper at full speed. If so, there is a maximum speed (which varies somewhat with load) beyond which a stepper will not accelerate, and this speed is normally well below what you can reach with a gradual increase in speed. Google on "stepper motor torque curve".
The problem is that, with a 4-phase stepper such as you are using, if the shaft angle lags more than 2 step angles behind the commanded angle, the torque reverses and the motor sits and vibrates and makes horrible noises. This is not, technically speaking, a stall condition, where the shaft does not move at all.
The torque-speed curve for your motor can be found at http://www.kelinginc.net/KL34H2120-42-8AT.pdf and indicates that the motor can be run at 5000 steps/second, which suggests that your problem is your attempt at fast start.
If, on the other hand, you've already tried a slowly increasing step rate while running, then you probably do need a heftier motor. However, my calculations for a .144 hp motor at 10 rps gives about 2 Nm torque, and the linked torque curve for your stepper is about the same, so I wouldn't expect a problem. Unless, of course, you've modified your mechanical setup somehow.
Best Answer
If you lower the current, you lower the torque. If the torque is insufficient for the load, you miss steps.
As you increase the speed, two things happen:
You could do any of these things to attempt to remedy the problem: