I have seen these variations in source DICOM images acquired using identical sequences. In some cases, this might reflect tiny sequence adjustments to handle different angulations, or it may just be rounding errors from the scanner. This explains why dcm2niix includes a tolerance for slight variations. My sense would be not to change the values reported by the scanner, but consider a tolerance when deciding if these values are truly different.
Thank you for the advice.
My concern at the moment: if I were to include RepetitionTime: 0.0081 as a criteria in the dcm2bids configuration file for this particular scan, would dcm2bids treat these as separate scans?
It will be seen as separate scans in the config file but if you point it to right direction it will be seen as a T1w the same way you did for the one with "RepetitionTime": 0.008112.