I was trying to do exactly the same thing in VS 2010 (.net 3.5). It turns out that you can do this using the Settings designer. The UI is totally flawed, as stated, but if you manually enter the fully qualified name of the enum in the Browse window it’ll work. This has the benefit of not modifying generated code (*.Designer.cs), which is always good to avoid because when you do there’s no guarantee that you’re changes won’t be overwritten.
PS – This only seems to work if the enum is public.
Settings GUI:

Then manually type fully-qualified type name:

At one point I swear I saw a drop-down of the enum values in the Value column, but I haven’t seen it since and you just have to type an appropriate value in.