A3977 is really only suitable for 2A in continuous machine use. It's really a little SMD driver for use in bubblejet printers and other low duty applications.
A larger more rugged unipolar IC such as the SLA series will support 3A at continuous use, and have a proven track record for reliability. You also get the benefit of better high speed performance than bipolar series and less resonance than bipolar parallel.
My personal recommendation is the SLA7062 as used in this high performance unipolar driver;