Well, I emailed Goodyear to ask if I could mix A2s and A3 and amazingly a really nice chap from technical support called me back and talked to me about it for about 30 minutes. In the end his conclusion was: 'maybe'. And he asked me to let him know how it went!
He said that A2s were radials but had a bit of something cross-y in them which stiffened the sidewall. A3s might also have that, or might not. So there might be a difference in sidewall stiffness.
Also, he said that the regulations allow a great deal of latitude in tyre sizing so a 285mm tyre from one company might actually put as much as 300mm onto the road (really?!?). And so mixing brands might result in unexpected
actual sizes. Here is a helpful chart:
And he said the real issue was not the rubber on the road but the computer in the car. He said that if the car had sophisticated (but dumb) computer systems, plus unexpected tyre behaviours axle-to-axle or (worse) wheel-to-wheel, then skid control systems might behave in inappropriate ways.
And he said that Dunlops (a Goodyear brand) were great for QPs, but it turned out he meant QP-IVs not QP-Vs.
And he said that Goodyear F1 Asymetric
5s are coming out soon, but it turned out not for QP-Vs.
I have no idea how much of this is valid. It certainly was not terribly useful.
I'm gonna try the mix....