It would have exactly the same deployment problems, but waste more bytes in every packet header. Proposals like this have been considered and rejected.
How is checking if, say, the source address is 255.255.255.255 to trigger special processing, any easier than checking if the version number is 6? If you're thinking about passing IPv6 packets through an IPv4 section of the network, that can already be achieved easily with tunneling. Note that ISPs already do, and always have done, transparent tunneling to pass IPv6 packets through IPv4-only sections of their network, and vice versa, at no cost to you.
Edit: And if you want to put the addresses of translation gateways into the IPv4 source and destination fields, that is literally just tunneling.
How is checking if, say, the source address is 255.255.255.255 to trigger special processing, any easier than checking if the version number is 6? If you're thinking about passing IPv6 packets through an IPv4 section of the network, that can already be achieved easily with tunneling. Note that ISPs already do, and always have done, transparent tunneling to pass IPv6 packets through IPv4-only sections of their network, and vice versa, at no cost to you.
Edit: And if you want to put the addresses of translation gateways into the IPv4 source and destination fields, that is literally just tunneling.