This thread is now moribund, but this comment still merits a correction. The Gulf Stream today is part of the surface component of the Meridional Overturning Circulation, which is the North Atlantic part of the THC. If the extreme scenarios pan out and the THC weakens or shuts down because of icesheet melt, then the Gulf Stream will continue, it just won't be carrying heat to N. Europe. That heat will remain in low latitudes.

If you look at the flow over N. America you will note that just past the Rockies the flow drifts to lower latitude over the Great Plains, then swings back up to higher lats over the Eastern Seaboard. That swing is driven by a need to conserve angular momentum; it helps that the flow would otherwise be blocked by the N. Atlantic subtropical high (aka Bermuda or Azores High, depending on season). That swing is also what drives the Gulf Stream.

Weather systems feed from that energy in the same way that hurricanes feed from the warm water of the gulf of mexico.

Weather systems over the US and Europe are extratropical cyclones, which are completely different from tropical cyclones (though one can morph into the other, usually tropical to extratropical). The former is driven by thermal and humidity differences between airmasses and is controlled by the polar jet (which of course is a boundary itself), the latter is a heat engine converting warm ocean surfaces to high wind and heavy rain and form within an airmass.