The points at Canal Tunnel Junction are right at the northern end of the tunnels. Given that the tunnels are single track bores, there's no chance of changeover until the trailing crossover just before Bell Isle junction, and a facing crossover inside Copenhagen Tunnel. There are trailing and facing crossovers each way between STP and Farringdon (ZFD) which are used when there are partial core blockades as is the scissors crossover on the ramp up to Kentish Town, but there is no way that anything than a 700 would be allowed down in the core anyway.
Aside from the prohibition and unacceptable operational issues if access was allowed, if Kings Cross is so bunged up, the Thameslink trains would be the key ECML route for passengers into London, so there wouldn't be room for faffing around turning Networkers (or 377s) in the core. Passengers on those would be ejected at Finsbury Park to continue on the tube, the Moorgate line or Thameslink.