First things first, have you looked at updating to v2.1 There has been a lot of work in the backup/restore areas so this may be something that can be overcome simply by updating. However:
Max execution time exceeded in home/*/lib/filestorage/zip_archive.php line 105
suggests the possibility that the value in the php.ini is not long enough to allow the script to finish. If you have some rather large graphics and/or video, then that may cause an issue. (I had one tiff file that was 42MB creating a similar problem when coupled with a video of 98mb and some other rather large files.) In that case, I suggest that you may want to break your backup into different parts, and ensure your restorations are sequential. That has worked for me in a v2.0.2 test backup/restore.