The first time I read your issue I thought you were affected by an issue that occurred with PHP Ondrej PPA some months ago, that would explain why you were seeing more than one PHP version installed. Webinoly immediately released a patch for that at that moment, in some rare cases re-installing PHP twice is necessary. Seems like it's not the case!
Now, I think you have a very corrupted installation and packages. In a very normal Webinoly situation, re-installing PHP would be sufficient. In your case, I have no idea why it's failing.
- You said that the stack command is not removing all the previous versions. That's not correct!
- You said that the stack command is throwing errors about "parent directories". That's not correct!
- You said that now no PHP package is installed. That's not correct!
In summary, you're seeing a lot of errors, at this point you should consider a fresh installation from your backups.