Would be nice to know what the duty cycle is between 1000W and 2000W. Assume that heat generated at 2000W would trigger the thermal protection, but how long would that take, and how long does it take to recover. If you know that you are operating below 1000W all the time then this would not be a problem. It would be appropriate if they claim continous and max that they give the duty cycles for various wattages. If 2000W max is for 5 seconds only then may not suit your needs. However if 1500W for 5 minutes is available and suits then you are on a winner.
Note that the duty cycle will depend on ambient temp. (fan cooled so will need some ventalation) and how long the inverter has been running for (and at what wattage). At 45C it will not operate as long on 2000W then at 25C. Also it will not run as long on 2000W if it has been running on 1000W continously as opposed to being turned on to max (2000W).
On the temp. thing, did it provide the details of temp. range as this may effect the continous and max output wattages. I could not see any details.
For me if they do not provide the details then it would be best to buy bigger than required (number or capacity) and use that to compare prices. May not be as big a saving but may provide better reliability.