Is there a way to get to partially uploaded files?
As already suggested in the comments, it's is not worth wasting your time trying to do some magic with PHP.
HTML5 already supports chucked file uploads, it would be a much better approach to use some sort of JavaScript library or something else that relies on this technology. I can recommend FlowJS (the demo speaks for itself), but if you don't like it - I am pretty sure there are plenty more around the web with the same functionality.