I have selected full width in the component however the slide show only spans the width of the TEMPLATE module.

If you are using GANTRY & Rocket theme templates. Here is a quick fix for you . 

#rt-drawer div.rt-container
{
    width:100% !important; 
}

#rt-drawer div.rt-container div.rt-grid-12
{
    width:100% !important;
    margin: 0 auto;
}