Seems to me that "unless he can change the game somehow" is exactly what is going on. A new election would not be the traditional Labour vs Conservative contest, it would be a Brexit vs Euro contest with crossover support from both of the traditional parties. Currently the party structures are not set up to support this new alignment (maybe LibDem is), which is why (if you ask me) an election will not solve anything.

The more interesting question is what will the party lineup be after the Brexit or non-Brexit decision is finally taken (if we are still alive to see it). The Workers do not seem to be very enthusiastic about taking on The City at this point, so maybe the new alignment, or maybe even a third alignment, might persist--and the Labour and Conservative parties thrown onto the ash heap permanently.