Plane / Planes / Aircraft / Aeroplane / Airplane appreciation

I wonder if F1 technology could be used to push rpm and therefore screw speed?

Any billionaires (developing a complete new high power piston engine wouldn't be cheap) out there with an interest in an esoteric record could certainly get more power from a piston engine of a given mass and frontal area, those WWII era engines were good at the time but there are gains to be had from better combustion chamber design and reduced parasitic losses from gas flow. There are existing single airscrews capable of channelling 11,000hp aboard the A400M, so a complex and heavy gearbox to produce contra-rotation shouldn't be required (although the torque reaction will be a handful, so there is much computation needed to see whether the contra-rotation kit is more of a handicap than the trim drag needed to keep your aeroplane flying straight). At 17'5" diameter they are going to need some lengthy oleo legs, but that's not insurmountable, and anyway you're probably looking at scaling down to about 5,000hp and about ~13' propeller diameter to hit your 900km/h target. Designing your airframe from scratch to exploit the new power pack should get you some useful drag reductions too - the fighter based racers were designed to carry a couple of tons of armour and armament, and the stress calculations were simplified to allow them to even be done without high speed digital computers, and they were built from weaker alloys than are current in 2015, not to mention that you could use carbon fibre. You start getting into the kind of virtuous circle which allows the 70% scale S51 to do 275mph off only 400hp - lighten the airframe, cut the wing area to suit, which lightens the airframe, which lets you cut the wing area etc. Of course, you tend to end up with a GeeBee, i.e. some wings bolted onto the sides of an engine, but that's racing.