I was having similar problems. I have multiple testing sites in use on my local machine. Each one is a migrated version of the next. All of a sudden, I started running into export stalls (stalling a 0%, at 95% or even at 100%) when using All-in-One Migration on each of these sites except the original. Some had previous successful exports and some did not. I was always exporting to File.
On opening and comparing the wp-content folders for each site, I noticed that in every site that was giving me problems, there were strange folders present in the wp-content folder (ns/meta; w3.org; different for every site and some much more than others). I deleted these folders in each of the problem sites, tried to export again and it worked just fine every time.
I’ve no idea what caused the problem. But this fixed it.