Angus,
the vmax of the Me163 Komet was 960km/h(around mach0.8) in 3000m altitude, although the rocket produce more thrust and the air get more thin in higher altitude the Komet wasnt able to fly faster in a level fligt in higher altitudes, cause the as colder the air get, as higher the machnumbers get. The Me163 had max climbrate (tank almost empty) of around 150m/s, what mean, this is a vertical climb.
With other words, tha power of the Komet(almost empty tanks) was stronger than the gravity. While a dive it couldnt get much faster, cause it simply dont was controllable anymore, although it had a advanced highspeed wing construction(arrowed, very smal aspect ratio wings).
A propplane dont get any advantage out of its propeller at high machnumbers, cause the proppeller itself get earlyer into trouble than the plane, cause to produce thrust the propeller have to rotate faster than the plane fly. Actually the propeller will act much more early as airbreak, otherwise the engine simply would overdrive. In theory they could use a different reduction gear to overcome the engine max rpm problem, but still the blades would get supersonic problems and dont would be able to produce thrust. Therfor propeller driven planes cant reach mach1 at all and much earlyer they cant produce thrust anymore, so the result base on a free fall, the engine is only needed for the initial acceleration.
To reach mach 0,85 in a free fall is not very credible, but maybe they did add two tonns weight to increade the dragload, but i doubt a pilot(plane) would have survived this.
A stopclock and altmeter dont would help, cause the max speed only could get reached for some sec, a to short timespan to measure it in this way.
In general the highest to expect speed will be at 2000-3000m, here the drag due to thick air and lower mach numbers result in a minimum of drag, but here a pilot dont had much time left to pull up(specialy in a typical WWII plane).
They made divetests with a P51B(from 28.000ft), with removed propeller but metal covered elevators, and did reach machnumbers of 0,755. In a windtunnel they was able to reach mach 0,825(no propeller!!)
The P39N (much smaler wing aspect ratio) did reach max mach 0,8 while a powered dive from service selling(34.000ft), most trys was good below this(0,755 and 0,777).
Important to note is that they couldnt reach this speed with max rpm, they had to reduce the rpm, probably to avoid supersonic problems(increased drag) at the propellerbalades.
The resulting dragcoefficient at low machnumbers was a bit better in the P51(0,0215), as long as the P51 surface was clean, with a bit dust on it, it was worse than that of the P39(0,022) .
I doubt that a Spitfire was able to reach such numbers, it had a much worse dragload, what is most important. Maybe the heavy, late one, with clipped wings.
Greetings, Knegel