Hi – great question!
One approach is to add a conditional statement to the top of your template that tries to determine if a single event page is being requested or not and, if a match is detected, simply loads a different template.
Say you are using the default-template.php template (known as the Default Events Template in the settings screen) – you could override this (see here for details) and add something like this to the top of your customized version:
if ( is_single() && tribe_is_event() ) {
get_template_part( 'your/custom/single-event-tpl' );
return;
}
Does that help/would that work for you?