Yes, 11.4 is beta.  I do believe you can manually set the fan speed by creating custom profiles (editing them yourself or with a tool), but it's not a feature provided in the standard Catalyst Control Panel, and since I'm just doing this for fun, I don't really want to mess with something that might result in my card bursting into flames.  :-)

Having run 11.4 for about 24 hours now, I can now update my previous observation.  The fan isn't always louder.  It seems to be loud for an hour or so at a time and then can be quiet for many hours, then eventually gets loud again.  Not sure what is up with that.

I'd imagine there is probably some sort of tool I could use to monitor and record the fan RPM and the GPU temperatures.  However, I won't be going back to an older version of the drivers (since I'm upgrading to a 6990 on Monday), so this data would be in isolation as I wouldn't be able to collect similar data using the old drivers to see what the difference is.

Another difference is that the ambient temperature may be changing, since the weather is also starting to get warmer.  So it may not be due to 11.4 but because we've had a 10°C change in the outdoor temperature over the past three days.  The computer is in my basement, where the temperature should be relatively constant, but perhaps even a couple degrees would make enough of a difference to bring the fan to the next higher speed.  Who knows.  All I know is I can hear it upstairs, whereas I didn't used to be able to.