Hi dsttexas.
Sorry if there was a misunderstanding. 
dsttexas wrote:.......
Unless you suggest otherwise, what I had intended to was continue doing peridoc incremental manual backups against the new backup base, using SymNRA each time and save those log files. Hopefully one or more of those will be a good log file and I'll note those. Then if I see growth that seems unreasonable I will post back again and hopefully will have good log files to compare. If things go fine for some time (?), I may quit the SymNRA steps every time as they do add time.
Sound ok?
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Yes that sounds OK in principle. But I think it is important to try and see if there is an issue with SymNRA not producing reliable logs. So can you run a manual, incremental backup relatively soon and see if you can get a clean SymNRA log. If not report back here exactly what you did and what it said.
Once we can reliably get SymNRA logs it will just be a case of patience.... Keep an eye on the size of the backup set on disk and note if there are any odd size increases. Then make sure we can get a copy of the previous SymNRA log.
Should you decide to just give up with the laborious logging I will quite understand but it would be helpful if you could keep us updated here and let us know if you do decide to give up. That way we will at least know how long it was with no obvious error. 
dsttexas also wrote:.....
Another question too - does the backup of files that have changed cause a new copy to be added everytime, and old versions never go away? Hence, growth in the backup set would always get larger and larger compared to the source. Since a lot of what I do is with photos and videos, those changes can add up fast. However, the little work I did from my mid-March start until the backup set had more that doubled (adding about 1 TB in about 6 weeks) does not seem even remotely possible.
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I do not know if N360 keeps the old backed up files or deletes them. But I know of no way to get back to those earlier files so I hope they would normally be deleted and replaced by the newer ones. It will be interesting to see how you note your backup set changing in size on the disk. It may give us some ideas. What I have seen in the past is a glitch (caused by what I do not know) that caused what looked like a full new backup to be put on top of an existing backup. So the size doubled with only the one set of files being accessible. I do not know if this is what has happened to you. Hopefully we will find out.
Good luck.