I am coming into this in middle and don't have time to read the previous context, but ending the Gulf Stream warming of Europe does not require a change in currents or axis spin of the planet.
All it takes is for cold fresh water melt-off from Greenland to force the heavier warmer salt water of the Gulf stream to subduct down beneath the surface, where it is much colder.
That would prevent Gulf Stream warming of Europe, dropping temperatures there by over 10 degrees F. That is one of many ways how global warming can cause local cooling.
Another is by energying polar storms enough to leave their normal latitudes, and get much further towards the equator than they normally are able to.
Global warming means much more energetic weather, which can many more extreme results.
Global warming means more snow because there is more evaporated water vapor in the air to condense from winter weather. It is going to snow if it is 25 degrees or -25 degrees.
Temperature alone does not decide it it is going to snow.
The main factor in the winter is whether or not there is enough water vapor in the air.
And global warming greatly increases water vapor in the air.
If you've come in the middle, you didn't miss anything ...
The fresh water coming off the Greenland ice sheet would form a thin sheen over the salt water ... this is true ... it does seem to be enough fresh water to cause but minimal restrictions of the current ... gravity demands equal density for equal elevation, so the fresh water spreads out over the ocean as far as it can spread ... put a little gasoline in a puddle and you'll see what I mean ... plus I think you have cause-and-effect wrong ... for the cause of Europe getting warmer, the Gulf Stream slows down ... less energy needs to be transported, the forces transporting the energy weakens ... Europe is warming faster than the equator ...
Again ... with Arctic Amplification ... there's less force driving "polar storms" towards the equator ... although there's good research that the lobes of the polar front are increasing in amplitude, we still have the problem here in North America of these lobes rarely pushing over the Gulf of Mexico, they tend to stop "cold" at the Gulf Coast ... sometimes though, infamously the day they tried to launch Space Shuttle
Challenger ...
Global warming means much more energetic weather, which can many more extreme results.
This is a common misunderstanding ... global warming means more energy in the atmosphere ... however, weather is driven by
power ... power and energy are related, but they are different things ... put two 1,000ºC chunks of iron together, plenty of energy, but no power ... a chunk at 0ºC and one at 500ºC, less energy, but energy will flow one to the other, we have power ...
As the poles warm twice as fast as the equator ... less energy will flow, thus less average power in the atmosphere reducing the probability of more powerful weather events ... yes, more energy, but less power ... weather will be calmer in a warmer future ... that's clear cut for droughts, although with floods there's other factors involved ... where the flooding balance winds up in our warmer future is difficult to estimate ... maybe more, maybe less ... I'd avoid building your home ten feet below sea level all the same ...