And when you dismiss all data that doesn't agree with you-- which is what you're doing-- then it is completely impossible to ever overturn your conspiracy theory that all the science ever done on climate happens to be wrong.
In fact, it's not. This is currently the best hypothesis that fits the data, including the dates. There may be a better hypothesis later. This is the way science is done; you gather data, make a hypothesis that fits the data, and see if later work confirms or overturns the hypothesis.
Paleoclimate resesearch, and most specifically modelling the climate variations in the late middle ages is indeed difficult, because not only don't we have contemporary measurements of all the input parameters, we don't have good measurements of the temperature, either. (Modelling contemporary climate is much more accurate-- we have lots of data on both the input (the solar output is well measured) and the climate (not just average temperatures, but diurnal variation, seasonal variation, latitude and longitude variation, etc. all of which must fit the modelling, although the AGW debaters only ever look at the year-by-year changes.)
The paper referenced, however does use a pretty convincing proxy for temperature change in the little ice age: they looked at the dead flora preserved in the Arctic ice cap. This dates the little ice age to a start in 1375-1400, with a second cooling period around 1450 AD. That is about the time when the Vikings abandoned their settlements in Greenland (they kept Church records; the last document in Greenland (a marriage certificate) was dated 1408.)
Unfortunately, this is THREE HUNDRED YEARS before the Maunder minimum. So it's really hard to think that the Maunder minimum caused the little ice age.
So, here's the summary.
1. There is no well-understood mechanism connecting sunspot numbers to climate.
2. The only connection between the Maunder minimum and the little ice age is a rough coincidence in timing.
3. But the more detailed examination of timing shows that the little ice age started much earlier.