You can play with the settings in your Group properties.

Enable Autostart
Change Interval Time
in Option, you can try say: Revert to full when SSC fails...etc.

I have never had to do this, but I am sure it is possible

I would assume that to use the option "Revert to full when SSC fails" I would in fact need SSC enabled and running?
I at the time don't use that option but will look into it.
Thanks

There is no such option from NW. It follow schedule so your next backup will be level which is according to schedule. You can only override it manually (eg. on group level). Usually in environments where you have setup like yours you have backup team or management sending out emails to desktop owners to leave desktops on due to backup or they face consequence not to have it. In your case you might consider doing that and teaching stuff when full backup of their machines happens.

Or, it these are Windows boxes, do VSS snapshot during working hours and have them mounted on server and do backup then whenever you want (however, this is big change in approach I do not think it is applicable here at all).