It's early in the morning and I am still a little sleepy, but Gwillard's comment about "putting the power on the ground" is the key to reaching 600+ and 700+ mph speeds on the salt flats with a wheel driven vehicle.
In the end it comes down to developing enough thrust (through the wheels, eh?) to overcome the air friction drag and rolling resistance, saving some additional power (wheel torque) for acceleration. So, what limits the wheel thrust in this instance? Without doing the math, it is the coefficient of friction between the drive wheels and the ground surface, the normal force of the drive wheels against the ground surface, and the drive wheel torque at the required rpm. Again, without doing the math, it will likely require using the vehicle aerodynamics to provide additional down force (like a formula one car) to obtain the required thrust for these very high speeds. So, the aerodynamicist's challenge is to design for low air friction drag (low Cd and low frontal area), vehicle stability (especially at low subsonic, transonic, and supersonic speeds), and the necessary down force to maintain wheel thrust (traction). Once these requirements are quantified, the horsepower can be determined, and the race is on.
My guess is that a salt pan surface will be superior to a mud lake for providing a reasonable coefficient of friction. The dusty mud lake surface would tend to act like a bunch of ball bearings - not good for traction? So, then the challenge would be to find a salt pan surface long enough or have enough acceleration to use the known courses.
Getting back to the early 1950s calculations of the maximum 1/4-mile perfomrance, that was caused by only considering the tire friction, not the chemical/mechanical bonds with the asphalt achieved by M&H and Goodyear tire engineers.
