I do not like the term 'wake turbulence' when describing the wake of an F1 car, I prefer 'dirty air' as it is a much more encompassing term implying that there are many features. Namely, pressure deficits (total, static and dynamic), non-linearity (in the form of localized up-wash/down-wash and in-wash/out-wash) from vorticity from the rear wing endplates, diffuser endfences, various vanes and winglets... etc around the car which break down in the wake to form turbulence, as well as turbulence from boundary layers.
The key effect of the wake is from the dynamic pressure deficit (proportional to streamwise velocity squared) not turbulence or up-wash. Turbulence has been shown to be beneficial in some cases, and it's effect significantly reduces when boundary layers are turbulent, as in the case of F1 cars. The effect of dynamic pressure is that it squeezes the static pressure on the surface of the car towards Cp=0; as neagative pressure under the car sucks the car into the ground, increasing the pressure in turn reduces the downforce. Dynamic pressure deficit at the base of the car is localised around the rear wheels and underbody, hence why 2017 cars are finding it harder to overtake with bigger tyres and larger diffusers. Low velocity in the wake also increases the angle of the up-wash vector which effectively reduces the angle of attack of downforce producing surfaces.
The effect of a wake is not necessarily proportional to quantity of downforce created, if you create the downforce in the right way you can have high downforce with less wake effect BUT increasing the proportion of downforce from the floor is not the solution. Instead increasing the proportion of downforce from the rear wing is better. I did some experiments to quantify the contribution of rear wing and floor on the wake and found downforce generated by the floor drags the wake downwards and affects a following car more (another reason the effect of a 2017 wake is greater as the contribution of the floor has increased from ~50% to north of 60%), whereas the rear wing drives the wake over a following car. Increasing the rear wing vorticity also helped to draw in higher velocity flow from around the car while pushing the wake further up.
So onto my car concept. I would limit the total car length and therefore the space available between the wheels and ultimately downforce generated by the floor. The rear wing length is increased to 500mm with a span of 1m to increase its downforce and drive vorticity. This is draggy as a solution so I would have a totally active car; active wings, active suspension, and active cooling. The active wings would reduce drag on straights, which would also reduce up-wash in the wake meaning that as well as being able to follow in corners there would still be a slipstream effect. The active suspension should allow for slightly simplified aerodynamic surfaces as a lot of the effort in current designs is to produce consistent downforce as the car attitude changes around a lap. The front of the chassis is projected down to the ground allowing for a less compromised suspension set-up. Also the front wing joins the nose, removing the Y250 vortex and it's importance. Active cooling obviously allows a low drag package for running in free air but then allows the cooling to open when behind another car.
While there is a contoured underbody, this isn't to increase downforce of the floor but to reduce the effect of the wake on car balance. At the moment the floor design means there are two low pressure peaks under the car, and the front one is more affected by the wake than at the diffuser (as the wake becomes weaker further from the back of the car), where a wing shaped underbody will have a single low pressure peak and balance would remain consistent. Also a longer diffuser should produce less dynamic pressure deficit, especially if vanes and strakes are banned. Currently the short diffusers are over expanded with the multile channels and vortex producing vanes used to keep aiflow attached and generate a lot of downforce from the surface, to the detriment of a following car.
Sorry for the long post. I hope I explained this in a way which is understandable. Happy to answer any questions on my research if anyone's interested.
The latter was only introduced because it had become nearly impossible to overtake without it (and because the adjustable front wing didn't help at all 
).