exim is not accepting external connections

I'm still baffled as to why it just today stopped working, though.

Maybe your mail server had a busy day yesterday so the ISP noticed your abuse of the ToS?

Notice, that sending mail to another port would probably still conflict with your ISPs terms if it was running on some non-standard port, so I won't give explicit advice or recommend that to you.
I, for example, did receive a warning once from my ISP regarding "excessive" incoming and outgoing mail.

Discussing legitimation for this rule is something to do somewhere else.

You could, however, set up a cheap VPS somewhere to handle mail.
How to process that mail (directly on the VPS, or at home) is your task to evaluate.

Your remote node not necessarily needs to run its own mail server. Using a mail proxy like nginx - or even plain TCP proxying - would be fine, too.