Solution 1:

The only way I have been able to achieve this is by using NAT. Something like this:

iptables -t nat -A POSTROUTING -o eth0 -j SNAT --to 1.2.3.4

where 1.2.3.4 is one of your alias IPs. Doing this flips all outgoing traffic to use this IP address, for everything (so be careful).

You may wish to consider this variant:

iptables -t nat -A POSTROUTING -o eth0 -m owner --uid-owner user -j SNAT --to 1.2.3.4

I don't run this one myself, though I have tested it just now and iptables accepts it. This would allow you to have a per user/IP alias mapping (I think) so depending on the UID of the process running the socks proxy (I'm presuming here an SSH socks proxy, thus the user who is logging in via SSH), that IP will be used for any outgoing traffic.