I know it's possible to perform SNAT on outgoing packets and DNAT on
incoming ones, for purposes of IP masquerading, but is it possible to
perform DNAT on outgoing packets and SNAT on incoming packets that
match specific IP addresses, or specific IP addresses and ports? If so,
what do I need to do that, and how do I do it?

I have a client program which doesn't allow me to alter the IP/ports to
which it connects, and seeing as I can't compile from source, this
would allow me to connect to a different IP which is accessible and
that in turn connects to the server through port forwarding.

Using iptables in Linux I can accomplish this easily with rules
resembling:

iptables -t nat -A OUTPUT -p tcp -o eth0 -d 64.233.161.99 -dport 80 -j
DNAT --to-destination 216.155.200.155
iptables -t nat -A POSTROUTING -p tcp -s 216.155.200.155 -sport 80 -j
SNAT --to-source 64.233.161.99

which is what I would type to make it so that whenever I tried to
connect out to Google's web server, I would be connected to Altavista
instead. (This is just an example, my client isn't a web client.)

Right now my connection to the internet is through the LAN, behind a
router. I'm assigned an IP address over DHCP.

Thanks,
Matt