I’ve tried cleaning the charging port but it still won’t charge. Will connect if I hold it in tight.

In short, yes, the charging port can be replaced. You could call Apple or walk into a store—I am sure they'd do this for you, but it would probably be quite expensive. Third-party repair shops are not endorsed by Apple at all, but a reputable shop should do a good job for a lot less.

It might be a good time to look at a wireless charging mat (since iPhone 8 Plus supports wireless charging). It's not as fast or as efficient as a good old-fashioned plug, but at least you won't get stuck without a phone!