Your approach of having the "current" documents in the same place all the time should work fine, as long as you make them the easiest to find on your website. Then:
- They will be the most prominent docs on your website to Googlebot
- They will be the most prominent docs on your website to users
- Most links will be created towards the "current" documents
- Google will prefer the "current" version most often
I've seen Google's John Mueller recommend your "current" approach for "events" websites. For an event website, you would put the pages for this year's event on the main page and move previous years' pages to archive URLs.
Another approach to consider would be using canonical tags. You could mark the latest version of the documentation as canonical. Every time you release a new version you would change all the canonical tags in every version of the documentation to point to the latest version.
When using canonical tags, Google will only index one copy of your documentation. Users will always find the most recent version. If they try searching for an older version, they may not be able to find it.
Comparing the two approaches, the canonical tags are quicker. You could have the latest version in the search results in a just a few weeks. Your current documentation might take some time to get ranked well. You could hurry the process up by changing all the URLs for all old versions. Redirect all old versions to the current version and create new archive URLs for the old documentation versions.