While I love Oberlo I was really missing automatic synchronization of shipping times. This year I spent a some time and created a solution that automtically syncs Aliexpress shipping times with my store. This is how it looks now:
The shipping times are retrieved by setting a maximum price you are willing to pay for shipping. The software will then retrieve the fastest option that is below that threashhold. It took quite a lot of tweaking to get this to work, but in the end I think it integrates nicely (you can check the result here: www.deskgrown.com).
If anyone is looking to implement this into their store feel free to reach out! I will do it quickly as I have already gone through the pain of creating the software and learning how to integrate it. Just message me either here or to my email firstname.lastname@example.org