The Gyro is a tricky sensor to use, but at yesterday's FLL competition in Elk River, at least 5 teams had worked out the issues to their satisfaction. I'm revealing their answers here. It is unfair to those teams, since their research does represent a significant advantage over other teams. That said, none of their solutions were complete. Each team had some part of the answer, but none had everything.
One team, not one of the 5, had given up on using the gyro in the belief that it could not be place close to the rechargeable battery pack because the gyro sensor would get too hot. I hadn't heard that before and have no idea if it has any basis in fact.
Almost all of the teams used the "Simple Gyro Fix" mentioned in the original question. They varied in whether they paused before, during, and after each step.
Two teams had tests to avoid leaving home base with a "drifting" gyro. One waited 10 seconds to see if the drift was still less than 2 degrees. Another ran the robot through a routine that cause the robot to twitch if it was drifting. No twitching meant it was ok.
A different set of two teams added a double reset of the gyro. This reset being the reset of the Gyro angle to 0. One of those teams said they had followed the advice of some site on the internet. That team also added a 1 second wait before and after the double reset. The first to "still" the robot; the second to ensure the zeroing of the gyro angle had been taken.
One team had a set of MyBlocks that turned based on either the rotation sensors or the gyro sensor. It allowed them to retreat from using the gyro sensor if they needed to. They had gone to the trouble because of the bad reputation of the Gyro sensor. In front of the judges, they used the gyro. It worked. Clearly, they had worried a lot and then figured out how to use it.
The teams differed in how they turned. Some pivoted, some spinned, and some accepted any motion.
One team used the gyro to go straight, sort of a proportional line follower with a gyro sensor instead of light sensor. They did not use it for turns.
None of the teams did the work of recording the drifting episodes to a file. None of the teams displayed a warning as a sound, a blinking light, or a message on the LCD panel before the robot left the home base.
None of the teams switch automagically to the rotation sensors when the gyro is known to be drifting.
None of the teams used #2 of the accepted answer.