Holey undercuts in anisotropic material that warps Batman!
I don't think anyone makes lower stiffness 5 axis machines. You wouldn't need the stiffness of most industry standard machines for wood, but you'd need the DOF. Maybe you can do it on a 3 axis mill with a 2 axis rotary table, but figure spending around $25k for a decent used 3 axis mill (maybe doable on a 3 axis router at $3k) and a whopping $40-$80k on a two axis rocking table.
Legit Solidworks license: $6k
Camworks: $15k
If you're not averse to having an unfinished part, you could do most of the roughing on a 3 axis router with the rest of the undercutting work with chisels or a good micromotor. Call it a $3k router to make a 1'x1' sized panel 8" deep.
CAD/
CAM at $8k (Solidworks + Sprutcam) and a really really magical
CAD guy to model it all. Perhaps you can do a mesh of points on an original part which would end up getting all the data you need for 3 axis roughing without having to hire a very expensive 5 axis CMM.
If you want tool changing, you'll have to go up to a decent used mill with tool changer.
Not a bad idea if you're making a lot of these parts. The roughing would make the hand work go a heck of a lot faster and you'd scrap a lot fewer attempts.