The L298 datasheet says you can parallel the outputs, but you must parallel channel 1 with 4, and 2 with 3. Unfortunately, the motorshield R3 looks to have been wired up the wrong way to do this, because it uses channels 1 & 3 for one motor, and 2 & 4 (instead of 4 & 2) for the other.
You might like to consider using this motor driver http://www.pololu.com/catalog/product/1213 instead. Not only can it handle 5A peak and 3A continuous, it also has mosfet outputs instead of darlingtons, so it will have a much lower voltage drop, run cooler, and be less likely to overheat. Altogether a much better device IMO.