Since the last conversion was in 2012, and based on what was posted on the TIIA board, it is highly doubtful that this distribution relates back to the taxable TIRA account. The error appears more recent, well after the entire value was in the Roth IRA. Accordingly, I see no reason that this distribution including the earnings should be coded other than Q.
One thing that hampers the 4852 approach is that your 1099R might not be clearly recognized by the IRS as a Roth IRA, although the Q coded 1099R you also received probably shows the same account. Otherwise, the 4852 is a mainstream solution (which I noticed is a supported form on one of the free file programs), while trying to use Form 8606 now when you have not been filing it in the past to track your Roth IRA basis, would probably lead to IRS questions.
The only way a qualified Roth would change to non qualified is the unlikely scenario of a disabled person overcoming a disability prior to 59.5, and their Roth becomes non qualified again. They would then have to again determine how much basis they recovered in the meantime to start filing Form 8606 again. Have never heard of such a case, but that is what you would probably have to do if you filed an 8606 to make the distribution non taxable under the Roth IRA ordering rules.
Maybe you can reach the tax people at TIAA.