gyros would be unreliable if they were not caged before doing anything acrobatic as they would most likely tumble.
if your flying on instruments and get in a situation where you are in an extreme unusual attitude you have already made a series of errors or in the case of combat been hit by enemy fire or decided to take extreme evasive action.
modern gyros seem to right themselves after a few minutes and the amount of error in their readings can vary a little or a lot.
the original question about instrument flying differences between USAAF and Navy flight training practices would be a hard one to answer.
the only guess i could hazard is that in actual conditions of instrument flight in combat beyond the training setting would be this...
if your in a situation where your aircraft is in an unusual position with no outside visual references it would be a good thing to know which of your instrument systems are compromised by this unusual position and which might be compromised by battle damage if taking fire. then get the plane in a position in which you are certain of its attitude and ability to stay in flight and then get out of danger if possible then out of instrument conditions as soon as possible and attempt to return to base.

Pretty good answer and lets develop it a little further in the interest of safety
First thing you have to realize is this: there are few instruments that you can depend on in recovering from unusal attitudes, namely, needle and ball, altimeter, airspeed. That is three that you can always depend on to work correctly. The vertical speed indicator is useless in attitude recovery, it is a TREND instrument only and has a lot of lag before it will show any reliable information.
Step `1, power off all the way, you don't want the aircraft accelerating any faster than it already is, chances are the aircraft if already beginning to descend.
Step 2, get the wings level relative to the ground, no matter if aircraft is pointing down or not. You do this by centering the needle on the turn and bank indicator.
Step 3- center the ball. of course you want to do step 2 and 3 at the same time, now the aircraft will be in coornated
fight confg!
Step 4- Stop the loss of altitude!! Do this slowly, by watching the altimeter and monitoring the airspeed indicator!
If you perform these steps timely and smoothly, you will recover the aircraft and regain control for continuation of the flight.
The pilot, when under going instrument flight training, should have mastered unusual attitude recovery techques
while ongoing his basic instrument control training.
What I always practice was this: no matter what the lesson plan was for that particular lesson, I always ended it with at least 5 minutes of unusual attitude recovery practice. If the student pilot has been taught and developed a solid instrument "scan", he/she will have no problem with this part of their training!
Last, but not least, someone mentioned the Kennedy accident! Everyone who flys as pilot in command should know what their personal limitations are as a pilot and if they don't, they are looking for place to have an accident!