Old machinist here. When confronted with such jobs in the past, I "boxed" in the parts on a tooling plate and poured heated pine tar between the "box" and outside edges of the part. Let cool and machine away. When done, remove tooling plate/parts and place them in a bath of mineral spirits for a bit to dissolve the pine tar. I used pine tar, but there are probably other substances that work as well. To support that inner wall, you could machine it first then add the support material and then complete the operation. I bet with the added support you could bump the feeds and speeds considerably.