I've yet to try it on the Internet, but in theory one could use the IPv4 header "loose source route" (LSR) option to possibly accomplish the desired goal. First, one must set the IPv4 source address to whatever IPv4 address you want to appear to be coming from, then insert the IPv4 loose source route option into the IPv4 options such that at least one of the IP addresses in the route contains your real IPv4 address. Then, so long as your host knows how to intercept the return packets (because your machine doesn't appear as the destination host, just as a router,) your packets can appear to be coming from somewhere else.
All of the above requires a bunch of special software (I write IPv4 and IPv6 stack testing software that does that sort of thing.) It also assumes the target stack responds by inserting the loose source route option into the return packet with the source route reversed. Some stacks do this, some don't, and some it is configurable.
Some firewalls screen out IPv4 packets containing the LSR option. So given all the above, probably not feasible.
Anyway, for what it is worth, that is the one IPv4 source address "spoofing" technique I know of that in theory allows full bidirectional communications with no need to hack into routing tables.
