When searching your options under the label 110 year rule, I use filter by ascending date of birth to get the ones coming up next to reserve. But the names that have only a year and not a month and day come up first. They should be after those having a month and day because they cannot be reserved until January 1st of the next year. I must scroll down through all of them (hundreds) until I come to the ones for the current month and day.
Sounds like a good research project is sitting there. 110 years ago is not that long ago and birth information should be readily available. I would think that most of those individuals that have only the year deserve more research to get that month and day on there which would be a better solution to the problem and truly identify each as an individual.
For example, in Utah birth records over 100 years ago are public records and birth certificates are freely available on line:
Regarding sorting, building in exceptions to standard ordering with 1913 being viewed as the date 0/0/1913 (which comes before 1/1/1913) is probably a lot more complicated than it appears at first glance.