For the record, the difference between Python 2 and 3 is probably a side effect of revision 050f0f7be11e. Python 2 copies data from the ExFileObject returned by extractfile(), while Python 3 copies directly from the underlying file.

The patches to the file reading class look good.

I would be a bit hesitant about the bit that reads all the file data in the next() method. I guess if someone had an uncompressed tar file with only a couple of large files, and they just wanted to list the file names or extract a small file at the end, reading all the data would have a significant impact. Perhaps there is a way to seek almost to the end, and then just read one byte or something.

Also, beware that according to the documentation, os.truncate() only supports Windows in 3.5+, so you might have to adjust the test if applying this to 3.4.