You should be able to achieve this by taking over and modifying the publish hooks.
Using Maya as an example, it works out the next publish version here:
Which calls the _get_next_version_info from the base publish hook.
This attempts to work out the version from the workfile and then see if that publish version is available to use.
You could modify the Maya publish hook so that it doesn’t call this method and instead uses a different approach to figuring out the version. You could, for example, create a new method based off _get_next_version_info that gets the version using the publish template instead.