many find Corbyn as toxic as Brexit

If that is their thinking, there is no hope. Prime Minister is a temporary position, can be revoked or renewed at almost any time, has some political power but works within the existing state institutions. Brexit, on the other hand, is a permanent change, subject to possible renewal on a time scale that probably exceeds a decade, and has reams of impacts that are not even partially under the control of the state.

Corbyn should be made PM in order to back out of Brexit, then he should be replaced by whoever can get the job. The tactics at this point should have nothing to do with whether you like any particular politician, they are (or should be) entirely about avoiding Brexit.

Seems to me, naive American, that politicians saying "we oppose Brexit but will not support Corbyn" are simply Brexiteers.