That looks like a nasty little part to build. But maybe not so bad with some fixturing.
Maybe look at some different insert geometry, maybe check with your tool vendor for recommendations. I would definitely use carbide endmills for the profile and interior work. Use the largest carbide bullnose (3mm R on the bullnose) endmill that would make the larger radii. I would rough it out with a rougher, then change endmills for finishing. I'm assuming you have a tool changer on your machine.