Strange MySQL replication error 1146 (Table doesn't exist)
Not too sure why still, but this problem disappeared after some of the troubleshooting steps I took to hunt down the culprit. Maybe it was the open files limit that caused the errors while opening the MyISAM tables, perhaps because of the high activity of other services running on the slave2 server, like Rackspace's cloud backup... But, whichever the case, replication has been running smoothly on slave2 off of my master server for a number of weeks already after loading it up once more with a fresh data snapshot taken from slave1 in the same fashion as described in my original question.

So, although unfortunately I can't provide a clear answer to the problem, I can definitely say it looks to have been solved. So I'm closing this post for the time being.