I'd like to see your thermal calcs, test data and pcb layout. The 28degC/W junc-ambient rating is based on the JEDEC51-7 standard board of 114*76mm (with vias to JEDEC51-5). Yours is only 14% of that area so your thermal resistance is much much higher (its proportional to area), probably at least 170degC/W allowing for all the other components on the PCB. With a total Rds of 0.8ohm you risk random thermal shutdown at 1A especially on the inner units on that distribution board. I'd certainly not consider using this product.

Adding a heatsink to the package will have some but relatively minimal effect, the thermal path is to the PCB.

I recommend you move to the A3979 chip. Its pin compatible, has an Rds of 0.5ohm and gives a higher microstep setting. The 3977 is an old design and due to be deprecated soon anyway.