I think my approach would be to machine as much of this part as possible from one side. Note the corner with green arrow (and the opposite side as well) will need to have a fillet at least as large as the radius of your cutter.
Once I've gone as deep as possible and completely finished the top side, I'd add maybe 4 tapped holes where the red arrows are. Then I would bolt the part to a rectangular plate of material by those 4 holes, and flip it over (hold by the bolted on plate), and finish the back side.
Yes... your part will have 4 tapped holes in it, but those could just be drilled and chamfered in a drill press and made to look like a "weight reduction feature".
PM