Thank you very much for your response. I hadn't previously seen anything but the video.
You are correct that the answer to this question seems to be in the section of the documentation on Launching.
multisession: Launches up to n background R processes on the same machine (where n is the number of processor cores on the system, minus 1). So if an AWS instance has only 1 core, n is 1. And the number of launched background processes is zero. Then there's multicore, which seems to imply by its name that more than one core is required. The final option, multiprocess, appears to auto-select one of the first two.
Hope I'm wrong, since Linux itself seems able to run multiple processes on a single core without letting one of them capture the entire computer for extended periods of time.
The best answer to my particular problem is probably to switch out the mailR package with a direct connection to the Amazon Simple Email Service API, which should be much faster. But I haven't yet figured out how to create the security token the API requires.