I've only ever played it in Chrome, since that's my main browser. I followed your suggestions, and haven't had a problem yet. I completed one round of the CTTH where I've had the most problems. Then I tried IE, and it wouldn't keep me logged in in the game window. I tried logging in 3 or 4 times, checking the "remember me" box, and it would keep logging me off after less than a second. Went back to Chrome, and it prompted me to resume a tourney that I hadn't started, don't know what that was all about. Also, I found out that when IE logged me out in the game client window, I also became logged out here on the forums in Chrome. I haven't downloaded Firefox on this computer, and don't really feel like doing so just to test this bug out... sorry.
Thanks for the quick reply, and I hope I'm helping out with my blocks of text.