What are some good ways to do this? Is it even possible to do cleanly?
Ideally I'd like to use packet headers to decide which server should handle requests. However, if there is an easier/better way let me know.
It's impossible for both servers to listen on the same port at the same IP address: since a single socket can only be opened by a single process, only the first server configured for a certain IP/port combination will successfully bind, and the second one will fail.
You will thus need a workaround to achieve what you want. Easiest is probably to run Apache on your primary IP/port combination, and have it route requests for IIS (which should be configured for a different IP and/or port) to it using mod_rewrite.
Keep in mind that the alternative IP and port IIS runs on should be reachable to the clients connecting to your server: if you only have a single IP address available, you should take care to pick an IIS port that isn't generally blocked by firewalls (8080 might be a good option, or 443, even though you're running regular HTTP and not SSL)
P.S. Also, please note that you do need to modify the IIS default configuration using httpcfg before it will allow other servers to run on port 80 on any IP address on the same server: see Micky McQuade's answer for the procedure to do that...