I don't buy this The generators have electrically excited field windings. Take down the exciter fields, and there is no electrical power output.
Generator fields can be taken down in milliseconds. A resistor to dump the inductive energy stored is of manageable size, vs. a resistor to load the entire generator output for a long period. Once you drop the exciter fields, you have a mechanically unloaded steam turbine, which still presents a risk of over speed.
SCRAM takes a few seconds, so the thermal output of the reaction can be halted in this time. But there is stored heat from the reaction left in the core. Plus, there is still power output, equivalent to the initial value of the decay heat release rate, typically about 7% of total thermal power output.
It may take a few minutes, or at best a few 10s of seconds to actuate a steam valve of the massive size which controls the turbine feed. Presumably there is an alternate path to divert this steam, such as to additional heat exchangers in the cooling towers, right?
What I anticipate would be done if the grid tie were severed, is that instead of completely cutting generation, within a few milliseconds the exciter field may be ramped down to reduce power output to 10-20% or so, while a resistor (of more manageable size vs. one able to take full power) is switched in. Mechanical braking can also be applied, to consume another 10-20% of the turbine power. Now you are not completely unloaded, but still under-loaded 60-80%.
The problem now consists of a transient turbine speed rise then decay to stop, based on the competing dynamics of combined partial braking and power dumping working against the time it takes to divert the steam. I would expect that this control problem has been designed and validation tested to death for any plant. But I am speculating a bit here (not about the generator field, but about how the power take down is accomplished. So, since you asserted that:
"power that gets generated has to go somewhere, which is the power grid. If the nuclear power plant's connection to the grid gets severed (by bad weather, in this case), the power still has to go somewhere, or else it melts down the connecting infrastructure, and eventually triggers a nuclear meltdown situation."
Then please explain why the situation as I anticipate it is incorrect, and things will go all to hell anyway?