I was not prepared for this. After one single tweet from Guillermo Rauch I could run tests for over 1000 sites.
The good: He tweeted it at 1 AM in the night.
The bad: My DB was on the free plan. I woke up and saw that my DB had no storage left.
After a few adjustments and bug fixes, it now runs smoothly without any issues.
The best: My AWS forecast says ~ $0.80