Handling anims.j2a of several megabytes isn't practical and even thinking about uploading 9mb files on J2O for every custom anims.j2a is crazy... what JazzSD needs now are basically three things, apart from those in the readme:
1. The ability to decide where your animations are exported to and what names they will have.
2. The ability to import .png files of different names and be able to select them from other folders.
2. The ability to make an auto-patcher for anims.j2a. This, I think, is more or less the kind that's described in the readme: 'Import/Export changes made to anims.j2a as a mod, which can be shared'.

Let me explain.
When you edit anims.j2a, you should be able to select an 'Create anims.j2a patch' option under the File menu. This would read through all the edits made, which set IDs, animations, and animation frames have been edited, and put in all the graphics data, along with where they should be in anims.j2a into a file. This file could have an extension of, say, .jsd, and only JazzSD would be able to read it.

Now, the .jsd file would only include the new graphics, NOT the whole multi-mb large anims.j2a, and it would probably be no more than 100kb large. When you include it with your J2O upload, the downloader can just open JazzSD, and select the 'Patch anims.j2a' option under the file menu, then select the .jsd file from a menu, and JazzSD would edit anims.j2a for you. This is slightly slower than just copying and pasting anims.j2a, but it takes up so much less space. You could even have JazzSD create mini-versions of itself (they would be executables), which only allow the patching of anims.j2a with the added graphics.

EDIT: I've seen the new improvements and updated my review. If you read it, you'll notice that I have found that the save function becomes useless when JazzSD still keeps its old save-technique. DON'T make the program save edits automatically, without permission, when it exits. DON'T make it save, without permission, when you switch set IDs. Is it possible to just keep the edits as they are and be able to work with animations in multiple sets at the same time?

EDIT 2: 'Exporting PNG' is mentioned twice in the readme. The second one should be, well, 'Import PNG'.