After many attempts, I discovered that it seems to be possible to center the ‘logo’ in LayerSlider:
In Slider Settings/YourLogo enter this in the YourLogo Style box:
left:50%; top: 10px;
The ‘left:50%’ does the horizontal centering – the ‘top’ is whatever you need as margin from the top of the slider.
Hoping this is helpful and proves valid across browsers!