My cat did that as a kitten-- she would do her business and then wam-- start to play with the litter like she it was a tunnel-- my husband would have to watch her-- wait till she was done with her business, praise her and then remove her from the litter box area---
As she got older--she still does the scratching along the sides of the box but no more tunneling.. I think the covered litter box would be the best bet for you
Mine seem to like to get everything ready for a long time, then cover up. Getting a cover helps a bunch, but mine still kick it out. We put old scatter rugs underneath to catch it and recently bought a litter catcher rug. I like the Tidy cats box and have plain Van Ness boxes as extras.