Hi Tom,
Looking into the latest log, I see that the log file was opened twice on resumption 10. This indicates that the resumption was fired twice, and is likely to have led to the zip errors (As data is added to the file out of order in this sort of case)
The cause of this sort of error is the scheduler not recognising that the process has been resumed. This indicates that the server is overloaded. You will need to talk to your hosts again I’m afraid, and ask them to investigate the load on the server.
Could you also try downloading the Uploads backup files (Through the Existing Backups tab), and seeing if you can unzip the file labelled:
backup_2016-01-01-2128_First_Evangelical_Lutheran_Churc_cf40609a8c59-uploads19.zip
Best Wishes,
David