You should take another look at the data sheet for the L298N. Specifically look under applications (bottom of page 7, top of pg 8.)
For continuous DC operation you need to de-rate the chip to 3-3.5A and parallel both H-bridges. Note that while the chip is a dual H-bridge, the motor supply (Vs) is all fed from just Pin 4. PWM is not straight DC but during rapid moves it will pull full current at near 99% voltage.
I have seen a few home brew PCB's that used 3x L298 in parallel and they worked quite well. There was still the issue of current limiting... The work around in that config was to have power supplies which maxed out just under the peak current.