Gearmotors wear out clutches and gears, and overheat easily due to the path for heat conduction out of the motor. They often come from the factory with sub-optimal lubrication type and/or quantities.
Sudden application of power and especially high motor temperature can damage them faster. A hot motor can fail in just a few minutes, the gears generally fail first. I don't know if you are monitoring motor temperature, but that is a good thing to do. That is perhaps the best indicator of danger.
It is hard to put a specific value on the power handling capacity of these motors. Finding consensus is difficult - there are many differing experiences here on ES. 1500W seems to work fairly well, perhaps a long time on a bicycle. 2000-2500W works but often fails, again on a bicycle. Putting one of these gearmotors on a heavier moped, and pushing it above 1500W is not likely to produce good motor life.
So you are already pushing it hard, and you are planning to push it harder. I can't predict when it will fail, but I would move ahead on the 3kW DD motor, it is better suited to your machine. You can look at my Borg (link in my sig) build to see something similar that I have used for many thousands of commute miles with excellent reliability.
I try to keep my full size gearmotors to 1500W or less, based on the supplier's recommendations for long life. It is actually motor current that matters more than power. If you have a controller that allows controlling motor current and smooth ramping to avoid rapid heating and clutch slamming things will last longer. A temperature sensor in the motor causing power rollback would really be excellent here, but I don't have that yet. I use Grin PhaseRunners on my Bonanza and am moving to that on the BikeE. The torque throttle control is also nicer than the usual PWM throttle controls for smooth and precise control.
Good luck with your project.
I see dogman added some excellent advice (and fairly similar) while I was typing mine.