This is probably stupid but couldn't you just turn on the auto pilot and get your hands and feet away from the controls and let the plane correct itself? Before ripping me apart I have zero experience with auto pilot so I'm assuming there is an obvious reason this wouldn't work.
Well, first, you have to actually have an autopilot. They are heavy, so if you want to haul some weight, they are a bad thing.
Second, most have bank, pitch and airspeed limitations. Either they will just turn off (if they know they are out of bounds), or they will not work properly (if they don't).
Third, a one-axis autopilot might take care of roll for you, but you still have to handle pitch.
Fourth, they don't work very well in significant turbulence. In a downdraft, altitude hold can fly you into a stall, and heading hold can lead to upset. If they don't just turn off due to exceeding limitations.
Fifth, you have to not override them due to your disorientation. It's harder than it sounds. Especially if the roll axis autopilot is making you more disoriented (it will wallow due to uncoordinated turns -- no rudder control in many light aircraft autopilots, even rather sophisticated ones).
IF you have one AND it works under conditions given, it may help. But there are circumstances where it just won't do the right thing.
Note that if you just use a default mode, many autopilots will hold roll and maybe pitch where they are. While that can keep it from getting worse (unless the pitch is far up or down), it's not the same as leveling the aircraft. This IS the mode most appropriate for turbulence, but you want to start it close to level, which may be difficult if you're disoriented.
When depending on an autopilot for safety, they have a tendency to turn off just when you need them the most. Particularly when their inputs get interrupted. AF447 is an example.
The biggest issue is that you have to realize you're disoriented. It's not as easy as it sounds. Vertigo is kinda obvious, but more conventional disorientation is a
wrong signal, not a scrambled one. That is, you're convinced the aircraft is doing something really different from what it is actually doing.