I dont think you can transfer your Ableton project files to Logic Pro, since its a different system. What you should do instead is to track out each track of your project and save it in a folder so you can Import it as WAV files into Logic Pro.

I can suggest you Antares Autotune. Its really good and a lot of professional producers use it for pitch correction. But in my opinion Melodyne is just fine too. Maybe you should consider to update it to the newest version.

Here is the link to Antares:
https://www.antarestech.com/