I was always taught, if it turns to poo in IMC, turn on the autopilot if you have one and buy yourself ample time to fix the problem and/or land asap.
Funny you should mention the use of the autopilot. Forgive yet another "war story or Warry" but in another era I was flying an old RAAF Lincoln bomber from Townsville to Darwin with an ETA an hour before dawn.
I vaguely recall we were around 8000 ft in cloud half way to Darwin at 160 TAS meaning about three hours to go. Without warning the one and only artificial horizon failed spectacularly leaving us with just the basic turn and bank indicator similar to that in a Tiger Moth.
Fortunately the autopilot was engaged at the time. I had done plenty of practice limited panel flying during our training on Wirraways but this was the first time for real. It was not a pleasant feeling to be in cloud for the next three hours on (very) limited panel. We arrived over Darwin an hour before dawn and still in cloud. ATC said there were lower patches but an instrument approach was available. That military instrument approach was called Lucero which was something like a bastardised DME arrival.
I wasn't game to try and hand fly that on limited panel or autopilot since the autopilot was a steam driven affair so that was out. So we simply twiddled the autopilot to fly in circles while still IMC until dawn came up and we could see holes in the clouds. We weaved our way through them and eventually saw the airport. It was that experience that made me feel grateful for the accent on limited panel flying during our pilots course on Wirraways.
Re limited panel practice in synthetic trainers. Although the sensation of turbulence cannot be adequately replicated in fixed base synthetic trainers, nevertheless there is inestimable value in practicing of instrument scanning techniques without an AH or gyro compass, since the scan pattern and scan rate can be quite different. Of course if the standby flight instrument is another AH and not a turn coordinator, then it becomes almost a non-event.