Ladder inheritance

Given:
 struct A0 {};
 struct B0 : A0 {};
 struct C0 : B0 {};
which are not to be changed, and needing the effect of:
 struct A1 : A0 {}
 struct B1 : B0, A1 {};
 struct C1 : C0, B1 {};
The goal here is that the X1 hierarchy should be topologically the same
as the X0 hierarchy, but with a few added members at each level. The
desired inheritance graph looks like a ladder:
 A0 <- A1
  ^ ^
 B0 <- B1
  ^ ^
 C0 <- C1

The obvious approach is:

 struct A0 { int a0; };
 struct B0 : A0 { int b0; };
 struct C0 : B0 { int c0; };
 struct A1 : virtual A0 { int a1; };
 struct B1 : virtual B0, virtual A1 { int b1; };
 struct C1 : virtual C0, virtual B1 { int c1; };
int main() {
 C1 cx;
 cx.a0 = cx.b0 = cx.c0 = cx.a1 = cx.b1 = cx.c1 = 0;
 return 0;
}

but that gets you (g++ 4.6.3):

foo.cc: In function ?int main()?:
foo.cc:10:9: error: request for member ?a0? is ambiguous
foo.cc:2:17: error: candidates are: int A::a0
foo.cc:2:17: error: int A::a0
foo.cc:2:17: error: int A::a0
foo.cc:10:17: error: request for member ?b0? is ambiguous
foo.cc:3:22: error: candidates are: int B::b0
foo.cc:3:22: error: int B::b0
(Comeau gives a better diagnostic but reports the same errors).

Making all the bases in the X0 hierarchy virtual avoids the errors, but
that's not an available choice in my use case, and in any case would
hose any other derivations that did not want virtual inheritance from
the X0 hierarchy.

Essentially I am trying to derive a whole inheritance graph from another
whole inheritance graph, rather than deriving a single class from
another single class. I expected that deriving from a virtual base class
would implicitly make all the bases of the virtual base be also virtual;
apparently not.

Is there any way to do this? If not, why was inheritance from a virtual
base defined this way?

--
      [ See http://www.gotw.ca/resources/clcm.htm for info about ]
      [ comp.lang.c++.moderated. First time posters: Do this! ]