Ryan I just happen to have a factory Scamp
overhead bin sitting on the floor of my basement and I checked - at its deepest point its 18". Its deep enough to take a few standard size pillows without a problem.
I would be reluctant to make them much deeper - especially the front one as I think it would pretty encroaching/imposing up front if where deeper. In fact there is only a few inches of clearance between my side bathroom wall and the cabinet as it is. Just enough room to slip my solar panel
in place for storage up against the bathroom wall and secured to it with bungee cords.
I am not sure about your year of trailer but one of the reasons that Scamp normally only puts in side cabinets at the rear of the 16' standard is the height of the rear window. I know they do put rear cabinets into the deluxe model but I seem to recall they are the same depth as the side cabinets and they can do it on that model as the window is a little different? may be incorrect on that - its possible the side cabinets are not as high instead. The bottom of the rear stock side cabinets in the 16' standard sit slightly below the height of the rear window - so if you where to put a rear cabinet in, the bottom needs to be higher than the stock side cabinet bottoms. The height between the top of the window and roof is pretty limited so I know a lot of folks have added a simple shelf between the two side cabinets for holding small items such as books etc.
Hope that helps - look forward to seeing pictures of your project!!