Plane / Planes / Aircraft / Aeroplane / Airplane appreciation

if the AOA limits are as low as the SR-71's appear to be during supersonic flight, it's not going to happen.

Yeah, that could have been put better - obviously there is some limit on the zoom climb potential, but you can still swap enough speed for altitude to comfortable top the Lightning acheivement. It's moot anyway, as other sources mentioned since have place the SR-71 in level flight at higher altitude at the end of the cruise-climb phase.

but a 'setting' that limits AOA on an plane of that era sounds unlikely. As far as I'm aware such things didn't (couldn't, even) exist until they put a computer between the stick and the control surfaces.

There was a computer, and it did push the stick forward if the pilot tried to exceed the AOA limit; it was all described in one of the earlier references. Two settings, one which was just a stick shaker and one which did the shaker thing and then forced the pilot's hand at the next stage. Not fly-by-wire as we now know it, as my reading of it suggests that the pilot could get into a tug of war with the system and still fuck it up if he wanted to.