After looking at some eagletree graphs of two high speed setups i came to the conclusion that 4.5KW shouldn't be needed for your small and lightwheight car.
Here is why:
. A 13.9KG (30.4lbs) 1:5 onroad car with 10s lipo, lehner 2240 needed around 4.5KW input to reach 95mph (145km/h). The graph can be found
here (site is in german)
. A Rustler VXL needed 1560 Watt for 82mph.
The graph
I know you reach for higher speeds and the faster you go the energy needed does not augment in a linear way. But i think you won't need 4.5KW at all. Your batteries should be able to provide it. I wouldn't count on a MMM to be able to provide 4.5KW. A high AMP flight ESC with slower ramp up time might do the trick as brakes might not be as critical for a speed attempt. If brakes are needed i would look into a MGM 22418 which should be able to provide up to 4.5KW. As you already stated those high power levels only last for a short period and judging from the posted graphes it seems as if your highest Watt peak will be shortly before you reach top speed. Holding top speed won't require as much power as accelerating.
Looking forward to see your final built and good luck with your speed attempt.