I'm transferring all my old DATs in order to discard them, and am glad that I had more than one player on hand. Of the two that I assumed would be the most reliable, one (a Sony DTC-75ES -- a full-sized "desktop" unit) crapped out entirely (wouldn't load tapes), while the other one (a Sony TCD-D10 Pro, which cost $2800 in its day if I recall correctly) clearly produces more audible errors than the less imposing, small portables. (That recorder is basically one long story of continuing disappointment.)
If none of these had worked, I would definitely have gone looking for the quickest possible replacement.