It seems like it wouldn't be that hard to create an indexed tar.gz format that's backwards compatible. One way would be to use the last file in the tar as the index, and as files are added, you can remove the index, append the new file, append some basic file metadata and the compressed offset (maybe of the deflate chunk) into the index, update the index size in bytes in a small footer at the end of the index, and ap…
Also gzip supports on-the-fly stream-based compression and decompression so anything requires jumping to the end to do reading and writing while compression/decompresion is no go.