This is something of a puzzle because if your technique is good enough to make a useful score in woodland, then it really should be up to the task outside one as well.
As I see it, the problem here is down to background, or more accurately, the lack of it.
A backdrop of trees gives the eyes and brain something with which to judge a target’s speed, angle and distance – something lacking when the clay is presented over flat ground and against the sky.
And shooting in woodland also improves focus in another way… it encourages us to pay closer attention to a target’s pick up and ‘kill’ point among the branches and clearings.
No background and given a full view of the target you are probably setting yourself up differently, maybe trying to shoot it a little later (or earlier) than you normally would, or being a bit too deliberate with the shot.
The only advice I can give is for you to treat these targets in the open just as you would were they in woodland: choose your pick-up point and kill area carefully, and don’t be tempted to rush the shot.
Equally, don’t slow down too much either – you might end up stopping the swing and poking at the target.