Actually, the EKET's internal height is 12-3/4", as is the width of each cubicle. The depth is 13". I have a fair number of boxsets, which fit in the EKET just fine. The only ones too tall for it are the MoFi 1-Steps and Analogue Productions UHQR's, but those have the LP's themselves in normal-sized cardboard jackets. I store the over-sized boxes in a bookcase; even if those boxes fit, I wouldn't store the LP's in them anyway: too much work to get the LP out every time. ;-)
One thing you absolutely want to do with the Kallax is to set it up with the full-width panels horizontal; the 4 x 4 version can also be positioned such that those panels run vertically. Some Kallax owners have not noticed that structural design element, which has led to some catastrophic LP-loaded collapses! Some owners have added a back panel, which not only keeps dust out of each cubicle, but also provides some additional structural integrity.