Good topic to bring up.
The main problem is that we don't have reliable data that goes back before instrumental records.
We really can't say exactly what the pattern/dynamics of the ocean circulations were during the Little Ice Age.
With regards to this causing another Little Ice Age, greenhouse gas warming would certainly offset some of that IF that were the natural cycle and if the drop in solar activity that we are currently experiencing is going to cause an effect similar to the Maunder Minimum and its period of low sunspots.
To be blaming a Little Ice Age on global warming is really stretching ones imagination.
If fresh/melt water from melting glaciers did cause a change to the circulation in the North Atlantic Ocean that did lead to cooling, I would say that it was just a negative feedback to resist excessive warming.
In fact, our planet thrives on negative feedbacks that resist rapid changes. The climate models are wrong by dialing in too strong of positive feedbacks. The increase in H2O for instance mean more greenhouse gas warming for the models.......but also more low clouds that block incoming shortwave radiation.......a big negative feedback that can't be known or put into models.
Anyway, if fresh water from melting changed the circulation and temperatures got colder in the higher latitudes because of that, then the colder temperatures would cause more ice to reform(less snow to melt in the Summer) and the glaciers would grow, the oceans would become saltier again and we would go back to where it was before.
Maybe this takes many decades to play out or causes effects that last for many decades?
But there is no "runaway" effect, getting out of control in 1 direction that gets worse and worse in most realms.
Obviously we had ice ages that lasted for long periods of time but we are talking about something different here. If solar radiation was reduced or increased by X amount, then we would also be talking about something different.
Even there, the earth's oceans and atmosphere would come to a new equilibrium, where the balance of heat coming in, equaled the heat going out.