You are correct in presuming that the outgoing mail account is based on the default that you set.
Personally I have never found a way around this as you cannot have numerous default emails, you cannot set a specific outgoing mail account to a request type, and you cannot use an action rule to send an email from a specific mail account.
This being said, there's always a possibility that a workaround has been found so don't give up yet!
Thanks for taking the time to reply! What you have said was my fear, as I couldn't find a way to do it either. I did consider having a more generic email@example.com to use for outgoing email, as this would mean any request type gets a more generic company reply rather than specific departments. However the trouble with that is that I'm guessing it would break the replies sent back to the ticket, as that outgoing account would not be an incoming one that accepts email.
Hopefully someone smarter than me has found some other workaround! Still open to ideas!