How do I deploy/manage similar sites from an unique profile, without dumps?
Features can help bypassing the UUID problem. It's still buggy, which prevents us from fully automating the process, but we can at least shift and maintain configuration manually.

Features still creates modules, it exports the configuration into the config/install directory of the given features module. This will be picked up when you install the feature, and you can continue to update your site config (similarly to what the old drush features-revert did) as your features export changes.

You can also import configuration directly via drush, make sure to use the --partial flag, to avoid overriding configuration not in the config folder. Using --source you can also define a custom configuration folder location, so you can do something like drush cim --partial --source=docroot/modules/features/myfeature/config/install.