I know of no GA aircraft used for training (C152, C172, PA-28, etc.) that does not have a published Va.
Personally I think there is way too much emphasis on Va as some speed, which if exceeded during any maneuver, is going to somehow result in a high probability of structural damage to the airplane. The key to maintaining the structural integrity of the airplane is to simply not exceed the designed load factor. This is the key, pure and simple. And in no way, in my opinion, is the worst student ever going to exceed 3.8 g's for normal category airplanes doing any of the private pilot or the commercial pilot maneuvers, even if they are totally botched.
Even when I do a normal aerobatic routine in my Decathlon that typically might include loops, rolls, Cuban 8's, reverse Cuban’s, hammerheads and Immelmans, I barely get to 3.5 G's. And as a matter of fact, when I begin most aerobatic maneuvers, except a snap roll, I am well above Va because I need the stored airspeed energy to complete the maneuver in a 180HP airplane.
So I would guess that Va is selected by the FAA for most GA certification maneuvers like steep turns, chandelles, and lazy 8's because there is some merit (almost none) for selecting this speed. But unfortunately the result of this emphasis is that many pilots blindly drink the “cool-aid” regarding VA as a speed that will do everything including guarantee eternal life in an airplane. Nice thought but Va isn't really that important an airspeed.
So as this thread started out discussing steep turns and Va, just pick any airspeed from VA to less than Va (unless the POH shows something different) and begin the maneuver. Hold that target airspeed plus or minus 10K as a standard. If your local DPE that you use says to do it at a lesser speed then you have no choice but to do it his/her way. Don't go any lower than 10K below Va though, because climb performance will be lost if the airplane gets low in altitude and a climb is necessary. Higher airspeeds represent stored energy that can be used to a pilot's advantage when required.
Your questions or comments are welcome……..