While reloading httpd did increase MaxClients to 400 as specified, it did not increase ServerLimit to 400 as specified. What is worse is that since ServerLimit remained at 256, this caused MaxClients to be reduced to 256 since ServerLimit seems to be the hard limit for MaxClients.
Even more frustrating is that when I did a service httpd restart, it not only did not increase ServerLimit to 400, but it threw an error that the attempt to increase ServerLimit during a restart was ignored.