I finally solved this problem for custom UTIs. First a little background. Our apps have two or three custom file types. They have been in the apps for at least five years and have always worked fine. After upgrading to iOS 13, users could no longer import their files from any source.
After trying many suggestions in this thread, I finally decided to delete the entire "Exported Type UTIs" and "Imported Type UTIs" keys from the info.plist for each app. Note that I used the property list view for all changes, not the source view. Next, I went to the target info tab and created new Exported UTIs and Imported UTIs. The identifier for each UTI was the same as before, which was the reverse company domain and the custom file extention (com.company.ext). The "conforms to" field was set to "public.data" for all. In the "additional properties" area, I added the UTTypeTagSpecification key as a dictionary and added the "public.filename-extension" key as an array. In the array I added one item which was the file extention.
UTTypeTagSpecification Dictionary
public.filename-extension Array
Item 0 String ext
Prior to these changes, I was working with the plist source to try to solve this problem. But apparently using the property gui editor changed the plist source in a way that resolved the problem. I only did a quick compare of the old file and the new and didn't see anything obvious.
Also, note that I did not make any changes to the Document Types.