You already answered this question above:
‘Yes, there is a hardcore faction of Labour MPs who genuinely would prefer Theresa May to Jeremy Corbyn as Prime Minister. Their public argument is that Corbyn is unelectable; privately, they would argue that even if he wasn’t, it would be wrong for him to become Prime Minister.’
If you want to control the opposition, be the opposition.
This is not the time for relationship counselling. The voters, however “uninterested” are not in fact children. No need to stay together for the kids. Voters can happily tell them all where to go without being traumatised for life, if they are but given the opportunity.
So if these people are so sure that the Tories are a lesser evil then they should put their money (and not the Labour Party’s) where their mouth is and tell people why, during the general election campaign… and those that don’t fancy their chances in the “neo-realist/Cynix party ” should remember what their job is and get on with calling the current unelected government to account.