I can see you have a great deal of first-hand knowledge that I don't, and yet positioning of weight away from the centre of mass of anything can't help but reduce its ability to turn. It is like the difference between a best grade British shotgun and an imported copy of very similar weight and similarly located point of balance. Suspend both of them by threads, force them out of the horizontal, and the former will return to horizontal faster and after fewer oscillations. It even works with mine and a very good Spanish double, although mine is nineteenth century, and only George Gibbs's third quality sidelock. The difference is in moment of inertia.
Supercharging is about as old as internal combustion, and turbocharging has been used in aircraft since WW1. Undoubtedly turbo lag is what made it very useful for bombers, but unacceptable for fighters. Bell tried it with the Airacobra (incidentally an ingenious solution to the moment of inertia problem), and found themselves with an aircraft unsuitable for high altitude combat.
There is an interesting benefit of the turbocharger. Being linked to the engine only by a column of compressed gases, generating that boost imposes very little stress, and the engine is stressed only by the increased power it produces. With the mechanical supercharger quite a bit of power must be taken from the engine to drive the thing. This produces a considerably higher increase in power, so your net profit is the difference between them. The stress imposed on the engine, however, is the sum of the two.
Funny things certainly happened to the controls of the fastest piston-engine fighters in power dives, but I think that was at least partly due to flexure, and actually coming even close to sonic velocity couldn't happen. The problem of propeller tips approaching sonic velocity is much more pronounced, and a serious danger, with helicopter otors. For on one side the airspeed of the rotor blade is the difference between rotational velocity and the aircraft's airspeed, and on the other side it is the sum of the two, with each blade alternating rapidly between them.
Perhaps the biggest snag with the Griffon-engined Spitfires (and the Spiteful, which was little if any more different that the late Spitfires) was fitting enough airscrew to use the power. Even slight increases in undercarriage height still required five blades. I don't think any Spitfire used contra-rotating propellers, although the naval Seafire did. They were used in the Martin-Baker MB5, though, and this was a very interesting aircraft. It incorporated many lessons which had been learned, offering much improved visibility and a speed of 460mph as a prototype. It had the P51's under-fuselage radiator, and was exceptionally easy to repair.
Test-pilots' reports were extremely good, and it could have seen wartime service, but I don't think it was any mystery, as Martin-Baker's own website says, why it wasn't adopted by the RAF. They had done some extremely good design work, including a rear-engine monoplane in 1934, and Britain's first eight-gun fighter, but they had never brought an aircraft into production. I believe it was thought that jets were the coming thing, and meanwhile conversion to high production of a recently-established small company was a lot riskier than asking Supermarine to improve the Spitfire.
http://www.martin-baker.com/about/mb1-mb5