The problem is we have Apache running on the same machine and Apache is our prime HTTP server (I like it, kill me ;-)). Anyway we managed to change IIS port but then OWA and MS Exchange Console stopped working. Don't really understand why, especially because OWA was working through https and we didn't change SSL port for IIS.
I'm just hoping there is a way out of this...
You're going to create Exchange headaches trying to mess with the HTTP bindings for Exchange services.
If I were you I'd either move Apache to its not on the Exchange server, or if you've got no choice but to leave it there then add another interface/IP and bind Apache to that other IP so they each have their own IP's and can listen on the same ports without conflict.
http://briandesmond.com/blog/redirecting-owa-urls-in-exchange-2010/
can you not create a redirect rule in your apache config to redirect any requests for exchange to IIS on that port / url ? you can get some idea from the link above.