That makes one wonder, what's so special about these 45 values? I think it would be far closer to "the end of the quest" if that could be determined, and those could also be handled by the rest of the algorithm somehow.
10^23 is not exactly representable in IEEE 754 binary64 format (aka double). 10^23 - 3 * 2^23, 10^23 - 2^23 and 10^23 + 2^23 are exactly representable however, so any number from 10^23 - 2 * 2^24 to 10^23 (inclusive, because IEEE 754 has a specific rounding mode here) is round to 10^23 - 2^23. Clearly the shortest correct output in the range would be 10^23, but 10^23 is the midpoint between two FP values! Both Grisu and Errol use a fixed size mantissa (64 bits and 106 bits respectively) and have a conservative error margin as a result, and that margin would always contain such midpoints.
Errol uses more precise error analysis to show that pathological midpoints are always integral and in the specific range. Since the specific range is <= 2^131, it simply tries to calculate the midpoint as a 128-bit integer and works around the conservative error margin. This removes a major source of pathological inputs, but the conservative error margin still exists and numbers may still fall in that hole. The final enumeration shows that there are only 45 such numbers.
So, how can we make sure that such numbers are converted correctly? The answer from Steel & White's paper is to perform arbitrary integer arithmetic and leave nothing up to chance. The Grisu3 algorithm by Loitsch showed that 64-bits correct converts about 99.5% of numbers. As you increase the amount of precision, you can improve your accuracy, but there is no guarantee that even 128-bits or 256-bits is enough to correctly convert all numbers.
Instead of trying to be 100% correct, our algorithm sidesteps the issue entirely by enumerating all failures a priori.