As UnionNine said, there is no way to define to MeshCAM where the plunge occurs, so it is a crapshoot. This is how to implement his workflow. (I had actually thought this up before reading his post so it might not be exactly what he had in mind…)
Make the box to the full height and the interior to the full depth, and open out to one end at the level of the bottom of the slot:

Make a second STL file, to the full height of the box but without the interior, but an open-ended recess at the bottom level of the slot and with the length and width of the slot:
Make a pencil-only finishing path with this second model, geometry only, zero margin, don’t machine top of stock.
The second workpiece must be aligned to the existing box workpiece like this:

If MeshCAM makes the initial plunge outside the original workpiece, this will cut the groove with the slotting cutter shown above. But there is no way to enforce the location of the initial plunge, Reversing the workpiece left-to-right might influence where the plunge is, but I have not done that experimentation. The cutter actually needs to be the full height of the groove (Woodruff cutters are the most useful), or else you need to repeat the pencil cut while fiddling with the depth.
But the straightforward and guaranteed way to do the box is in two simple pieces. Here is the lower piece
and here is the upper piece
and when glued together you get this
It is all simple top-down machining. Note the green arrows in both screenshots. You need to put a radius on the standing rib on the bottom piece to allow for the cutter radius on the top piece.
A further note is if you use a slotting/Woodruff cutter for the one-piece design, the radius at the closed slot corners will be much larger than in the two-piece design.