What you need is a
smart host, and a lot of ISP have it.
ISP that block port 25 usually allow relaying on their SMTP servers from internal lines, thus offering a smart host service, because that permits to have a control on what is sent from their customers without blocking it completely.
Read the "Use in spam control efforts" section of the
smart host Wikipedia page, call your ISP and ask for it. If they block port 25 without offering that service, you probably can bitch about it because it's not professional at all, and they will have to comply.
If their support section doesn't know what you are talking about, just try "smtp.ispdomain.example" and "mail.ispdomain.example" directly as smart host, it will probably work. Search for "exim smart host" on Google to learn how to set up your MTA.
There is absolutely no way to have a complete and working SMTP outbound service without having access to port 25 and without a smart host (yours, as I suggested in my first post, or at your ISP). Forget about it.
Oh, and one last thing. ISP block port 25 usually only for private customers, because of spam zombies. Private cable (or ADSL) customers usually have dynamic IP addresses. With a dynamic IP address you can't have DirectAdmin. If I'm right, you are on the wrong forum.