Probably the cheapest and best option is to build more wind and not care too much if it increases curtailment.
Yes, all the things mentioned should be looked into and done when it makes financial sense but "wasting wind" is much less a thing to worry about than "burning gas", and I'd rather waste wind than waste money.
https://xlinks.co/morocco-uk-power-project/
Surely HVDC links between Scotland and England could be built?
And then there are pumped hydropower storage project like this one with a proposed storage capacity of 200 GWh and 1.5GW of power:
In the worst case, couldn't the excess power simply be used in electrolyzers to generate hydrogen? They may not be very efficient but it's better than throwing free energy away.
why would this be necessary when the entirety of Great Britain is one synchronous grid?
Because there are bottlenecks in capacity on the synchronous grid that restrict the amount of power that can be moved from north-to-south (or vice-versa).
It works out better/cheaper/easier to bypass those bottlenecks with efficient undersea HVDC links than to try and build more terrestrial AC transmission lines.