Intruder,
Logic suggests to me the Vy will give better obstacle clearance over trees following an engine failure for a number of reasons.
* The aircraft will be higher - meaning it will glide further and longer - creating a larger landing footprint.
* The aircraft will have traveled further - meaning the available landing footprint will be further in front of the aircraft.
* If it is only a partial engine failure Vx and Vy will become closer together - it is far easier to decelerate from Vy to maximise performance than to accelerate from Vx.
* Whilst the aircraft will be lower in the very early part of the climb (due to loss of climb performance due to acceleration) most of that energy would be able to be converted to height anyway.
Granted prior to an engine failure climbing at Vx will increase the chances of outclimbing the trees in front.
I agree with your analysis. My earlier point was that IF the obstacles are a real concern, then Vx will help ensure initial clearance of those obstacles. Once clear, then Vy is preferable.
One thing to add, though, is that if a return to the airport is decided after the engine failure, use of Vy will shallow the climb angle overall, giving less margin in the glide back to the runway. Using your term, the available landing footprint BEHIND the aircraft is reduced with Vy.
Still, for most light singles, I would use Vy for initial climb. The performance difference between Vx and Vy is not that significant in most cases, and overall fuel economy and engine cooling are enhanced at the higher airspeed.