How do I change the outgoing SMTP port?

That should be a setting on your mail server software...and then you'll have to configure your mail clients that will receive mail to use the same port. You should be able to choose just about any open port you want.

You know, now that I think more about it, I think you'd need to have an SMTP relay service outside of your network. Since your server is sending mail to any other mail server, it will have to use 25, because that's where mail servers listen for incoming mail.

The other problem you're going to have is that a lot of servers will reject anything coming from a residential IP address, so a lot of your outgoing mail is going to get flagged as spam, or blocked outright, by the receiving server.

Your other alternative is to upgrade your internet connection to business class, then they won't block your ports. They don't block it to prevent spam getting to you, they block it to prevent spam going out from their IP's, which prevents their business customers from getting blacklisted by the spam blocking services.

So there's no way to send with other ports? You HAVE to use port 25?

Sure there is - talk to every mail administrator of every domain you might ever want to send mail to and have them reconfigure their mail servers to listen on some arbitrary port number that you define. Wait for them to do it (it shouldn't take them too long), and then you're done.

Oh, no, hang on a minute... none of them are going to do that, are they?

But that's what you're asking for - you're asking for them to accept mail on some non-standard port number just so you can get around Verizon's mail blocking.

There is a reason why standard port numbers (defined by IANA) exists - just so that everyone's talking on the same page (or at least in the same chapter of the same book). You can't arbitrarily pick a port number and expect it to work unless both sides of the connection know to use it. You know port 25 works for SMTP because that's the standard. You can use any port number you like for your own mail because you can configure your own mail client to use a non-standard port, but you can't convince the rest of the world to follow suit (at least not without good reason).

In this case your options are to relay your mail through Verizon's servers, upgrade to their business plan (which supports hosting your own mail server and doesn't break the user agreement), or setup another mail server somewhere else that you can relay your mail through.