No credible design is possible, because when people ask for a backwards-compatible IPng what they're really asking for is a forwards-compatible IPv4, and they can't have it because v4 isn't forwards compatible.

IPv6 is backwards compatible with v4 in a great many different ways. You've got dual stack, Teredo, 6to4, 6rd, 6over4, ISATAP, 6in4/4in6, NAT64/DNS64, 464xlat, DS-lite, MAP-T/E, 4rd, LW4over6... you could make a reasonable argument that it has too many methods of backwards compatibility, even. But obviously v4 isn't forwards compatible with it, because v4 isn't forwards compatible with any longer address length, and the time to fix that was in the 70s.

That's not something that can be changed without replacing v4. In fact, if it could be, we wouldn't need a new protocol in the first place.