Set batchsize on export form from server to server, or import from json.
The problem is that when you have big documents (over 1MB), default export reaches the 16MB limit and stops.

To be more specific, you should set the limit on how many documents should import/export.

Lets say that you have 1000 documents export of 5MB each. You should be able to export 3 documents to another server in order not to reach the 16MB limit.

So the progress should show some like: 3/1000, 6/1000, 9/1000 .... ....