I believe the blade on this cutter is “V” shaped so you would always get a little bit of over cut on a corner, never a sharp 90 degree corner, that if it is like the Jakar one I have. Even my Logan mount cutter kit cuts with the blade at an angle so would always get a bit over over cut.
Can you draw out a plan of your dimensions ? Based on your dimensions I am imagining a base in landscape style with the rectangle cut towards the bottom, middle slightly off centre to accommodate the box spine. Have I got the right ?
If that is the case the maximum width that would need to go through a die cutting machine would be the 240mm - if I have that right there are definitely machines that can accommodate that size. Admittedly they might be pricey but they are out there, but then everything is these days. Accucut machines come to mind. Most of the paper-crafting machines deal with an A4 size with the short side 210mm going through them. I will ask a crafty friend if she knows of any larger die-cutting machines.
I could also direct you to a Brother Scan-N-Cut machine which is a digital cutting machine that can deal with 305x610mm dimension paper/ card. The most up to date range (SDX) have an auto sensor that removes the need for the user to set the machine, so it can sense and move automatically between cutting vellum and construction card.