I use aliases (FastMail's term for custom addresses that go to the same inbox) for that reason. They work very well, and I've never had any problems setting up a new one on the fly.
I should have known they offer this sort of thing. I tried spinning up an alias in the past but was unable to find where to do so. Maybe the UI has improved since I tried ~year ago.
They did shuffle things around about a year ago. Aliases are under Settings, in the Admin section.