Never once had a problem with Fax over SIP, must be your SIP provider. Anyway simple answer to your question is that if you set automatic timed change between day and night mode, you can leave early and use one of the other modes to forward the call. When the time comes for the change to normal night mode it will switch modes. If you have too many alternate destinations, use a mode to forward it to a spare extension and then just forward that out to the one you want.

One of the issues I have seen preventing a call forward external is that the system is set to forward the caller ID but the carrier won't allow a different caller ID than the one associated with the line (to prevent spoofing). However I can't off the top of my head remember what you should check, maybe one of the other guys here can suggest what to check.