If I look again on your slider I'm not sure if a date is really suitable to create a slider with 12 month between min and max. Months and even years are not homogenous over a longer period and therefore the selected range might not always fit exactly. I could imagine that a period-field is more suitable.
I'm not sure if I understand correctly. The fields that I use are link_date_YYYYMM, I don't see how any other date field could change the problem. For example I could use link_date with all the dates, but that will give the same range except that I need the user to select by month.
This is what I mentioned above that a daily level won't be homogenous enough to select a period of 12 months over several years. But you could use a period-field for it mayve created within the master-calendar with something like this: