Seconded. Load testing tools seem to either be the "hammer with a single, anonymous GET request" or jMeter which is capable of anything but painful to work with. There are some other tools out there but the lack of documentation makes it hard to tell what you can and can't do.

Definitely! Not something we could have done properly in 48 hours though :)

A test that would use 100 lambda functions in parallel from each of the 4 regions and run for 5 minutes would cost about 3 USD. That should achieve a concurrency level of 100,000. That would be the most expensive test possible at the moment. Smaller tests are basically free.