why not just built it with a variable fillet? front is a fillet on the corners then the bottom edges minis the very back edge you run a small fillet and then with the same operation make your larger fillet as a variable and then finish up with the rest a as a small fillet. so make a box with three fillets.
If the arch at the back is the most import criteria then I would do a simple loft of two lines, trim the loft for the front radius make it's mate as a plane loft the two planes together (leaving enough room for a fillet) and then fillet the whole thing.