If you ask for a backfiring determination the form they will fax or e-mail you is the "Currency Transaction Reporting Backfiling or Amendment Checklist." (The form is unnumbered, unpublished, and my copy is May, 2012). If you made the same error on many reports on the same customer; e.g. the TIN was off by one digit, a "backfiling determination" would be appropriate. If you made a variety of different errors on the same customer it would not.
In choosing between the two alternatives it appears that FinCEN gave you, I would consider the fact that the regulators generally consider backfiling determinations as "you found it, you fixed it" and do not criticize the bank as a result. Filing 16 unsupervised corrections doesn't merit the same analysis.
In the subject line you mentioned "amending CTR's for the past year." I assume that means the errors began a year ago. If they began before that you would go back to the date where they began. There is no guidance that says you would only have to go back a year in filing corrections.
As for those you filed below the threshold, there is actually a mechanism for deleting reports from the system. It would be more appropriate than amending them. Personally, I would not know how to get the system to accept a CTR for an amount of less than $10K... That would include an amendment.
There was a relevant thread on deleting CTRs in this forum in recent months, but I cannot locate it in the time I have available.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.