It could be that you are looking at some outdated documentation (if you have a minute, I’d love to take a look to make sure it is current!) but you should definitely be able to shift your variants around. It’s a feature that all Unbounce accounts should have.
You may need to go to the overview screen and then change the “Page Traffic Mode” to A/B Test (even if you are not necessarily planning to run an A/B Test), and then from there you select the three little dots next to the variant you want to promote. Once there, select “Add to Test,” and then you should be able to promote it as your new champion.
Here’s a GIF of what this looks like!
Feel free to give me a shout if you’re still having trouble!