Yes making the app copy will not allow the extra files but the app copy is to test with to make sure you don't completely break your production app. You would copy the app like that and then work in the copy to understand the steps it would take to do it for production.
Moving the table like I mentioned can work for this but the new relationship needs to at least be similar to the old one. If it would be similar I can help with more advice on how to migrate the table over. If it will not be similar then that is going to be tough. By similar I mean you still need a way that works to identify what records belong to who and what they relate to as well. So transferring the table to a new app you then get to define the relationships again and pick the reference fields, which can be different than the old ones, but need to still work with other Related fields there too. It can get complicated depending on how many relationships you have or want to remake.
Moving a table I don't believe there is a file limit or if there is it is really big. The table I moved had 43GB of attached files.
The other option would be downloading all of your files and figuring out how to relate them in the new app, this would mean uploading them all again too. You can do this by creating a report including the file attachment field on it and having an extension like DownThemAll download everything in the report. This works but if you have related data that goes with the files it isn't as good.
There is also this script by Dan but it is a little bit older now. I have not tested it, it may or may not work. It does what you are requesting though. In the same thread there are other paid options as well that are listed too.
https://community.quickbase.com/communities/community-home/digestviewer/viewthread?MessageKey=db2c28cd-0b87-47dd-afb0-b7f2ff474ea1&CommunityKey=d860b0f8-6a48-487b-b346-44c47a19a804&tab=digestviewer
