Yes, an identity should solve it, it's possible for an identity to share the outgoing mail server or have its own.
Replying would be a bit of a hassle (having to choose an identity), but it's a workaround.
( I wonder what those ISPs / mail providers are thinking? "here is your email service, part of our $99.95 special package, but you can only use it while on our network... traveling, at the office, went outside? why would you want to do that?" )
Seriously, I might get around to it sooner or later, but so far, there are more pressing things to work on.