Placing 'Stinger' Transition

I've created a 'stinger' transition that lasts 1 second, and exported it so I can bring it in to other projects.
In the original project, I can place the transition clip anywhere. However, when I'm using it in other projects, I can only place it 1 second from the end of the first clip, or right at the start at the adjoining clip. Even after I create a compound clip of the two, it restricts where I can place the transition clip over it.
The transition fills the screen at the 0.5 second point and this is where the clip should change. Placing it before or after still results in a clunking switch between the two clips. How can I place the transition so the middle of the transition clip lines up with the point when one video clip ends and the other starts?
In the original project, I can place the transition clip anywhere. However, when I'm using it in other projects, I can only place it 1 second from the end of the first clip, or right at the start at the adjoining clip. Even after I create a compound clip of the two, it restricts where I can place the transition clip over it.
The transition fills the screen at the 0.5 second point and this is where the clip should change. Placing it before or after still results in a clunking switch between the two clips. How can I place the transition so the middle of the transition clip lines up with the point when one video clip ends and the other starts?