Still, I have a problem and would like it fixed.
I don't blame you. The personal visit you had might have had something to do with your age. Bet my iMac that if you were older the experience might have been different.
Also you can try a different Genius. They are capable of taking the machine and sending it off (if need be) and they CAN run it up and try to duplicate the issue.
A few tips, calm and curtious, nice always wins over rudeness.
Make an appointment to be seen, have an adult with you if need be, explain in detail what you have done, who you have talked to, and if you get to the point where they start it up, try to duplicate the issue. I know you said random times, but maybe you'll get lucky.
Also ask if you can boot in target disk mode with one of their known good OS X disks, then try to duplicate the issue again.
Something to mental note is when did all of this start happening? Did you install something and THEN it started, if so it might be an app. Follow?
Definitely if you feel one genius is giving you ***** you CAN ask for a 2nd opinion or have their manager present during the conversation. Remember, they're here to assist us, so a brush off or runaround is unacceptable.
I have never had anything but good experiences with anything Apple Care related so not all of it is like what your going through.
I wish you luck.