It's all about energy management.
You are still adding the same amount of power (energy) to the equation - you can either convert that energy to height (potential energy) or convert it to speed (kinetic energy).
If you accelerate in ground effect to say a cruise speed and then the engine quits you still have to stop. If you plonk it on the ground at 120 knots the Dunlops will do bugger all to stop you - the wing will still be generating lift severely limiting braking capacity - and that's the best case if the tyres survive the landing.
Ok you can pull back on the stick to convert some of the kinetic energy to potential energy, but that defeats the purpose of your proposed technique in the first place.
IMHO once obstacle clearance is no longer an issue, accelerating to and climbing at Best Rate will give you the most options if the fan stops. It is a very efficient airspeed - you will lose less energy through drag and will therefore maximise the time before you have to land. In most light singles Vy is reasonably close to the best glide speed as well.
The other advantage with a lower airspeed is that it reduces the radius of turn for the same bank angle, or from the opposite perspective it reduces the amount of bank to required to land in the same area that is not directly in front of you. Once again this will give you more options.
When an engine fails in a SE aircraft the insurance company buys the hull at this point and not when the aircraft is stopped. The aim of the exercise is to maximise the survivability for everyone on board - if the best way to achieve this will result in the aircraft being destroyed so be it. However on the same token putting the aircraft down undamaged will result in everyone surviving uninjured.
One of the big debates is when to retract the gear in a SE aircraft. One theory is to wait until you can no longer land on the remaining runway and stop before retracting the gear. The other theory is to retract the gear as soon as you have positive rate of climb. The advantage of the second method is it gives you a higher rate of climb and therefore more energy in the bank (more time, more options) if the engine stops. OK it increases the risk of landing with the wheels retracted on the runway, but from a survivability perspective very few people are injured in wheels up landings.
JT you beat me to it - but surely climbing at best rate would give you the best chance of clearing the trees wouldn't it?