The problem, Owen, is that the right simply don’t want to take the olive branch that Jeremy has offered time and time again, so a split is all but inevitable. As to whether Eagle is a Blairite, well, actions speak louder than words and her actions are those I would expect of one of slimy Tony’s acolytes.
The key seems to be that a large number in the party seem to have more in common with the Conservatives than with their own party’s socialist principles, so the only option left is for them to leave/be kicked and at least have a smaller number of MPs who represent their members. This is Blair’s legacy and final gift to his mentor, Maggie — the destruction of the Labour Party. May he rot in hell.