Anyway I was mulling it over and I have a solution to both leadership contests! The problem is both Labour and Tories have been simultaneously trying to convert the opposition while not abandoning their core supporters and in the process failing miserably. So the solution is simple: we need new parties. Specifically:
Old Tories: right-wing Tories. The pro-Leave chunk of the party that keeps threatening to defect to UKIP.
New Tories: left-wing Tories (in as much as such a thing exists). The pro-Remain chunk that merely tries to privatise everything.
New New Labour: right-wing Labourites (again, in as much as such a thing exists). Labour minus the unions.
and finally, New Old Labour: left-wing Labourites. Labour minus everything else.
Jeremy Corbyn gets New Old Labour and his challenger (probably Angela Eagle, whoever she is) gets New New Labour, while for Tories I think Michael Gove for Old and Theresa May for New is the most likely lineup (in the absence of Boris and David Cameron).
There you go, problem sorted! Each party now only has to please one chunk of voters and as a bonus the crazy is neatly corralled into the two Old parties.